This thread will present the stepwise development of a phase-detect autofocus system, using basic optical concepts and ray diagrams. The intent is to lay a solid foundation for the reader, to understand concepts critical to autofocus optics and operation, at a level which is visual, intuitive and readily understandable. There will be some mention of mathematical concepts that apply, but a working knowledge of them is not required in order to follow the discussion and diagrams.
See the following posts for presentations of each step in the development. More posts will be added later, as I have time, and/or in response to questions. The initial posts cover the fundamental optics for the AF system, starting with a single lens, then adding more optics to complete the AF system optical model.
There are many misconceptions associated with AF system behavior, as it is not always intuitive. Some readers may have difficulty accepting the system characteristics described, and ask for supporting references. The best reference I can give, is an optical system that I have sitting on my table right now, configured as detailed in the first few posts: It functions exactly as specified in this thread. I will post some details of that system, and photos of its operation, at a later time (taking photos can be easier than constructing theoretical diagrams, anyhow).
Suffice it to say that this thread will present more than purely theoretical concepts. It is my hope that this will be both fun and educational.
All optical systems need to start somewhere, so let's begin with a single lens. In addition to the usual considerations, though, I'd like to discuss another aspect that is important in autofocus optics: What I refer to as the "phase plane," also known as the aperture plane.
Here we have the familiar double-convex lens, its object plane, and image plane where focus is achieved:
The object planes and image planes are completely interchangeable. You may place a subject at either one, and an image will be formed at the other. Hereafter, I will often refer to these planes simply as "image planes" regardless of whether an object, or an image, is placed there. The lens works by providing a straight one-to-one correspondence between points on its two image planes, and does so in a well-behaved, linear fashion with (ideally) no scale variation.
Now let's think a bit about the light rays at the plane of the lens itself. The first fundamental concept is that you can take any small area on the lens, and the light rays passing through just that tiny area can form a complete image. (Anyone who has worked with holograms will be very familiar with this concept. Holograms use wave phase information - interference patterns - to encode an entire image at every elemental area on the film.)
All of the rays required to form a complete image, are passing through the small area on the lens plane. How is the image information represented? Each point on the image (or subject) has a unique ray angle associated with it, that is, the ray angles "encode" the image. In many applications, angles constitute "phase" thus my term for this plane is "phase plane." A mathematical operation known as the two-dimensional Fourier Transform can convert phase-plane information to image-plane information, and vice versa.
The only difference between the image projected by the entire lens, and the image projected by any small area of the lens, is the image brightness. In both cases, the image will still be complete, even if we chose a small area that is off-center.
Now, if we consider all of the small areas on the lens plane together, we see that there is a large collection of rays, constituting a somewhat complex light field. Think about this: What if we had a way to precisely duplicate such a light field artificially? If we placed a lens at that light field, it would be able to project an image from it.
When you're comfortable with that idea, go on to Step 2.
Now we get to do something apparently destructive: Take a thin diamond saw, and cut the lens into two sections, along its central plane, and polish the surfaces nicely. That makes two plano-convex lenses with the same diameters as the original lens.
Line the two lenses up on the same axis, with a wide space between them. To restore our optical system to its former operation, what could we do? Think about that phase plane again: If we could transfer the phase plane produced by the left lens, to the surface of the right lens, then it could project the same image that it did before, when the two lenses were still one.
If that sounds too difficult, rest assured that it's not. In fact, it's a perfect job for another convex lens, and we then end up with a system of 3 lenses. As it turns out, a lens is not only capable of projecting an object to an image, but it's also perfectly suitable for projecting one phase plane, to another phase plane. Let's inspect a few of the rays to see how this works.
Choose a lens with a focal length that is 1/4th of the distance between the two plano-convex lenses that we made with the diamond saw, i.e., the distance between the plano-convex lenses is 4f, where f is the focal length of the third lens we add, placed exactly between the other two lenses. Call this third lens the "field lens" since its job is to transfer the light field from the left lens, to the right lens:
By inspection and symmetry, we see it's possible to select any point on the left lens, and a pair of rays coming from that point, through the field lens equidistant from the optical axis, which arrive at a corresponding point on the right lens (same point, vertically inverted). Additionally, the angles of the rays have been precisely duplicated, since the rays form a parallelogram around the field lens. Since we now have rays arriving at the right lens, at the same (vertically inverted) point, and at the same angles that they had leaving the left lens, the light field has been duplicated. The right lens must be projecting the same image that it did before - except that it's inverted. (The inversion won't cause a problem for our AF system, as long as we allow for it.)
Our system of 3 lenses has five planes which are significant to us, but which have slightly different meanings to the three lenses:
1. At the far
left, the left lens object plane.
2. At left lens center, its phase plane - which is also the field lens object plane.
3. At field lens center, its phase plane.
4. At right lens center, its phase plane - which is also the field lens image plane.
5. At the far right, the right lens image plane.
There is a relationship between the field lens focal length, and the left/right lens focal lengths: For an AF system, we want the field lens phase plane to coincide with the left lens image plane, in other words the left lens is projecting its image onto the field lens. We also have the right lens object plane coinciding with the field lens phase plane. (Note the horizontal scale of this diagram is compressed relative to the original single-lens diagram.)
I should probably comment that with the three lenses spaced this way (left-lens image plane coincides with right-lens object plane), we could remove the field lens and the two remaining lenses would form the same image. However, the field lens still serves an important purpose, as we will see in the next step.
Note: If you are familiar with relay lens systems, you will notice some similarity. Relay systems differ in that they align image and object planes only, thus are much greater in length (it is their purpose to lengthen optical systems).
The next step will show the advantages we can obtain from the image/phase plane coincidences.
Here is where the field lens becomes especially important. Recall that its image planes are at the left/right lens phase planes. This means that it will project any object at one of those planes, onto the other. For example, if we take a Sharpie pen and write a letter on the left lens surface, then shine some light through it, the field lens will project that letter onto the right lens surface.
This will also work for an aperture. Let's add an aperture diaphragm to the left lens. The field lens then projects that diaphragm onto the right lens. In other words, a covering on any part of the left lens that will not pass light, will deny light reaching the corresponding part of the right lens. We say that the right lens has acquired a virtual aperture, which is identical in size and shape to the real aperture on the left lens.
This works in reverse, as well. Placing an aperture on the right lens, produces a matching virtual aperture on the left lens. Any light passing through the left lens, in the covered virtual-aperture area, will hit the aperture diaphragm on the right lens and thus will not reach the right lens. Conversely, light passing through the open area of the virtual aperture on the left lens, will hit the open area of the real aperture on the right lens, and thus pass through:
Since our system presently has left and right lenses that are the same size (let's suppose they're both 50mm diameter), the effect of a given aperture diaphragm on either lens will be the same: Stopping it down will darken the final image at the far right, projected by the right lens.
Now consider the effect of having real aperture diaphragms on both the left and right lenses, independently adjustable. If we stop the right lens down to only 10mm diameter, for example, all of the light from the left lens outside of its central 10mm will be rejected. In this situation, placing a real aperture on the left lens that is larger than 10mm will have no effect, as it's just blocking light that was already blocked at the right lens diaphragm. Thus we will see no effect from the left-lens diaphragm until it is reduced to less than 10mm diameter. Any larger diameters will not change the brightness of the image projected by the right lens.
Making a Couple Adjustments
In practical AF systems, the right lens - known as a separator lens - is quite small. Let's make our system more representative by changing the right lens to 6mm diameter. This is the same as placing a 6mm-wide aperture diaphragm in front of the former large lens, so the separator lens will only receive light from the central 6mm of the left lens. Now the brightness of the image projected by the 6mm separator lens will be much less than from the previous 50mm lens - but it will not be darkened further unless the diaphragm on the left lens is reduced to less than 6mm. The small separator lens also has a much shorter focal length, projecting a smaller image.
Another change we need to make, is to offset the separator lens from the optical axis, and add a second separator lens diametrically opposite to it. Let's offset these separators 9mm from the optical axis; then their circles will span from 6-12mm away from the optical axis. We also add a mask in front of the separators, to eliminate flare problems from rays that do not enter the separators.
Each separator will receive light from the left lens, across corresponding 6mm circles, also offset 9mm from the optical axis (since our system currently has the field lens centered). This means that setting any aperture diameter on the left lens that is 24mm or more, will not block any of the light reaching the separators. If we stop the left lens down to less than 24mm, the images projected by the separators will start to darken, and when the left-lens aperture reaches 12mm or less, the separators will receive no light at all.
In this diagram, the images of the separator lenses on the left lens (shown in gray) are the only areas that rays can pass through, and reach the separator lenses (rays shown solid). Other rays (dotted lines), not passing through the separator lens images, will miss the separator lenses at the right. The aperture diaphragm on the left lens is shown at nearly the narrowest setting that will not block light rays to the separators; if it is opened up more, it will admit more rays, but they will miss the separators:
In Nikon's AF systems, the separator-lens images are set just inside the f/5.6 circle. This diagram shows why lenses with maximum apertures larger than f/5.6, are not able to send more light through the separator lenses, to the AF detector, than an f/5.6 lens can.
As mentioned in the opening post, I have been using a real model alongside the theoretical analyses, primarily as a means of confirmation. It is also valuable as a demonstrator, and since I'm rather tired of producing diagrams, I thought I'd use some photos instead.
Here is the real optics model:
At the left is the AIs 105mm f/2.5, serving as the main imaging lens (aka "left lens" in the theoretical diagrams). The field lens in the middle is the AIs 50mm f/1.8, and the separator lens is the AIs 28mm f/2.8. As described earlier, the spacing between the main and separator lenses is 4f or 200mm (f is the field lens focal length, 50mm). The separator lens rests on a wooden cradle attached to a lateral micro-adjust slide, so I can set it to precise lateral displacements.
Virtual Apertures, Revisited: Subject Masking
We again apply the concept of virtual apertures, this time to the image planes of the left and right lenses instead of the image planes of the field lens. An aperture or mask at any one of these locations effectively "crops" the subject down, which helps to keep the images projected by the separator lenses from overlapping or producing flare.
Placing an aperture mask at any one of those 3 planes will effectively mask the other two as well, as discussed previously for the field lens object and image planes. It is usually most convenient to place this mask in front of the field lens. In the real model, we simply need to stop the field lens down. In practical AF systems with regular arrays of AF points, a rectangular mask is often desirable.
It's important to understand that adding this subject mask to the system does not darken the images projected by the separators; it just eclipses (crops) those images so that they cover a smaller area.
In this series of examples from the real model, we see the reducing aperture of the field lens cropping the AF detector's view of the subject (and you can clearly see the shape of the AIs 50mm's diaphragm opening). These are photos of the projection screen on the model, which simulates the surface of the AF detector:
For this demonstration, the model has been set up with the separator lens aperture diameter at 2.6mm (set f/11 on aperture ring), and the lateral shift has been set to 5mm. This places the separator-lens image just inside the f/5.6 circle at the main lens, as is standard in Nikon AF systems.
By taking a series of photos of the image projected on the screen (AF detector), as the main lens aperture is adjusted, we see when light starts to be reduced for the AF detector. This sequence starts at f/2.8:
We see clearly, that there is no change in detector-image brightness until the main lens is stopped down past f/5.6. At f/8, it is noticeably dimmer, and at f/11 it is no longer visible at all since the main lens aperture has completely covered the separator-lens circle in the main lens exit pupil.
AF System Effective Aperture
Since the AF detectors are receiving light through a fairly small circle on the main lens exit pupil, the effective aperture of the AF system is quite narrow, producing a high value for the focal ratio (f-stop). Although this makes the AF-detector image rather dim, it also has the benefit of yielding a high DOF or depth of focus for the AF sensors, which helps in determining focus errors when the main lens is far out of focus.
When a lens is focused at infinity, its focal ratio is given by f/d, where f is the focal length and d is the physical diameter of the lens entrance pupil. More generally, the focal ratio is effectively the lens-to-image distance divided by the lens entrance pupil diameter. Referring to the "Virtual Separator Lens" diagram posted earlier, we see that the lens-to-image distance for the separator lens can be taken as the distance from main lens to field lens, and its entrance pupil diameter is the diameter of the separator lens image circle on the main lens. For example, for the real optics model, the lens-to-image distance is 100mm and the separator-lens diameter is 2.6mm, giving a focal ratio of 38 - very high!
For commercial AF modules, we find that effective focal ratios run from about f/22 to f/32, for AF sensors that are set to the f/5.6 circle of the main lens (AF sensors set up for f/4 or f/2.8 can have "faster," or brighter, focal ratios).
Measuring Focus Error
We now turn to the ultimate goal of all of this optics discussion: How the optics give us a measure of focus error.
Forcing the separator lenses to view the subject from two different points on the main lens, which are offset from the optical axis, gives them an angled view of the subject - just as human binocular vision has. Because of the angled pathways, a change in the main lens focus setting produces a shift in the position of the two AF-detector images, towards or away from each other. For additional description of this, and experiments you can perform yourself, see AF Sensitivity and Function
As the main lens is focused closer, the two AF-detector images move slightly closer together, or conversely as the main lens is focused towards infinity, the AF-detector images move further apart. The real optics model only has one separator lens due to its large size, so we can only observe a single AF-detector image at a time.
The shift produced by changing main lens focus is surprisingly small. Fortunately, it helps that the subject masking (field lens aperture) gives us a reference position that does not move; we can compare the image to its fixed boundary. One additional complication with the model, is that there is also a noticeable change in magnification as the lens focus is changed from infinity to closest-focus, so it's best to look at the central point (nose) to see the movement. To help make the change easier to see, I have set the separator lens lateral position to use the main lens f/2.8 circle:
As the projected image in this example is only around 4mm wide, we see that the image shift is even less than 1mm - not much for a 105mm lens changing from infinity to 1m focus. One can imagine how small the shifts are for f/5.6 AF sensors when wide-angle lenses are used.
As a final point, note that in spite of the large focus change for the main lens, the AF-detector image does not go very far out of focus. This is a good demonstration of the advantage of the high focal ratio for the AF optics.
It's time to take a look at an actual AF system design. For the D3, we benefit from the sectioned-camera photo that has been widely circulated, which allows estimating the dimensions for the AF optics. From those, we can calculate a variety of parameters.
Our models have had the field lens in a symmetrical case, but in an actual camera where space for the AF module is very limited, the field lens must be used asymmetrically.
Dimensions we can obtain from the D3 photo are:
Field lens diameter: 10mm
Field lens to separator lens distance: 22.3mm
Separator lens to AF detector: 4.5mm
Field lens to main lens exit pupil: About 80-105mm (typically) depending on lens in use.
AF detector chip height: 6.5mm
We also know, from the spacing between the top-row and bottom-row cross-type AF sensors as they appear in the viewfinder, that the mask height for the field lens must be about 9mm.
We need to think a little more carefully about the locations of the separator-lens images on the main lens. These are aimed to fall inside the f/5.6 circle of the main lens exit pupil, so that gives the outer boundary. The inner boundary must be at f/8 or a little smaller. This means that the centers of the separator-lens images need to fall on about the f/6.8 circle of the main lens exit pupil. Thus it is the f/6.8 circle, rather than the f/5.6 circle, which acts as the baseline for the AF system.
Now we can calculate the following parameters for the central set of 15 cross-type AF sensors, which use 4 separator lenses (top, bottom, left, right):
Height of image projected by each separator lens onto AF sensor: 9mm * 4.5mm/22.3mm = 1.8mm
Separator lens spacing (top-bottom or left-right), center-to-center: 22.3mm/6.8 = 3.3mm
Separator image spacing (on AF sensor), center-to-center: 3.3mm * (4.5+22.3)/22.3 = 4mm
Overall height of the set of 4 images projected by separator lenses onto the AF sensor: 4mm + 1.8mm = 5.8mm (fits nicely onto the 6.5mm-high chip).
Also, we find the field lens focal length to be about 18mm and separator-lens focal length is about 3.7mm.
From the above, the figure that I want to consider next, is the height of the image projected by each separator lens, onto the AF sensor, which is only 1.8mm. This comes from an area of the main image which is 9mm high, in other words the AF sensor is seeing an image only 1/5th the size of the image at the imaging sensor. It's very small, and this has some consequences.
If we start with an in-focus image and focus the main lens a bit closer, or the subject moves a bit further away, the images on the AF sensor shift slightly closer together. The amount of this shift follows the perimeter of the blur circle in the image. Since the D3 has an 8.4um sensor pitch, we can just start to see the image going out of focus if the blur circle diameter reaches about 20um, or if its radius reaches about 10um. This 10um radius is how far each AF-sensor image would shift - if the AF sensor had the same image size as the imaging sensor.
Of course, it has only 1/5th the image size, which means the AF sensor needs to be able to detect an image shift of only 2um, in order to detect the image starting to go out of focus.
It Gets Worse
That 2um shift only corresponds to a main lens that has the same f-stop as we calculated above for the AF system baseline: f/6.8. A very fast lens, such as an f/1.4 lens, produces considerably more blur in the image for that 2um shift at the AF sensor. If we want to keep an image from an f/1.4 lens from going out of focus, the AF sensor will need to be able to detect an image shift of only 2um * 1.4/6.8 = 0.4um! That is only one-twentieth the size of the D3's image-sensor pitch.
I trust this will give you an appreciation for the precision required of the AF detector lines on the AF sensor. As an exercise, you may repeat the above calculations for a D800.
Today I received the D300 AF module that I ordered last week, and immediately set to disassembling it. The most important action was to remove the AF sensor from the top of the module, so I could place a "screen" there which allows showing what the AF sensor sees in actual operation. This was just a bit tricky, as the AF sensor is glued to the plastic module housing with epoxy (see how hard I work to show you guys this stuff)! I replaced the AF sensor with a bit of frosty cellophane tape which can act as a diffuser, or as a screen.
I have some interesting photos and measurements which I will share later. Right now, we'll take a look at the field lens doing its projection "magic." As you may recall from the early posts, the field lens projects the main lens phase plane, onto the separator lens phase plane, or vice versa. This also means that if an object is placed at one of those phase planes, its image will form at the other. The main function of the field lens, is to allow the separator-lens mask to be projected to specific patches on the main lens, which we want the AF system restricted to using.
To demonstrate this, I set the AF module up so it could project onto a screen (back of an envelope, which I thought was suitable since we have a "back of envelope" calculation to follow). Because there is no AF sub-mirror in this setup, the module sits in a different position, than it does when installed in the camera body.
I used a strong lamp to shine light onto the frosty tape (on top of the module) that's taking the place of the AF sensor; this light passes through the separator lenses and their mask, bounces off a 45-deg. mirror, then goes through the field lens, resulting in the separator-lens mask openings being projected onto the screen.
Here is the setup:
Here is a closeup of the mask images:
Note that only the center group of AF points has four separator lenses since they're cross-type points, while the outer groups of AF points only have two separator lenses (top and bottom). Thus all three groups illuminate the upper and lower patches, making them much brighter than the left and right patches. If you look closely, you can see some CA at the edges of the patches because all of these lenses are just molded plastic.
It's interesting to see that Nikon have made the patches somewhat elliptical, to increase their area and help with image brightness at the AF sensor.
Now for that calculation: The field lens was set 106mm from the screen (that's where it focused the separator mask best). The diameter of the circle circumscribing all four patches on the screen, is about 13.5mm. That means all of the patches actually fit inside the f/7.8 circle. In other words - in spite of what the owner's manual may say - this AF system is designed to be compatible with f/8 lenses. No wonder so many D300 owners have claimed that AF works fine when they add a TC-20 to their f/4 lenses! Sneaky Nikon. [In the case of the D3 AF system, I believe they have actually used the f/5.6 circle.]
Now let's place the AF module behind a lens with a well-lit subject, and send the light rays in the normal direction:
After moving the lamp so it wouldn't shine on the AF module's cellophane-tape "screen," I could photograph the images projected by the separator lenses. These are exactly what is projected onto the AF sensor chip (if we ignore the extra texture added by the plastic tape). The left and right groups of AF points each have two separator lenses (top and bottom) and project two images; the center group has four separator lenses, and projects four images. I took two photos, with the lens focus set differently; see if you can tell the difference:
Perhaps the most obvious difference, is the higher magnification when the main lens is focused closer. However, if you look closely (compare top to bottom), you can see that in the back-focused case, the images are a bit further apart than their border frames. In the front-focused case, they are a little closer together. If the lens were correctly focused, all of the images (for each of the three groups) would be positioned within their frames exactly the same.
The next post will discuss details of the module design, and the AF sensor.
Here are my notes and photos from examining a D300 AF module this week. Note: Some disassembly required.
As is typical of many contemporary AF modules, the AF-point array is divided into three sections. The center section contains the 15 cross-type points, and each lateral section has 18 points of unidirectional type. Each section requires its own field lens with mask, and accompanying separator lenses.
The three field lenses are molded as a single piece of clear plastic, and the mask has a single large opening for each field lens. The center mask is 8.4mm high by 5.1mm wide. Lateral masks are the same height, but 4.6mm wide, plus an outside "extension" of 1.8mm for the furthest-outside 3 points.
Here are the field lenses, after I reassembled the module. Please pardon the dust, and the slight distortion of the mask (I don't think Nikon would hire me to assemble their modules):
The field lenses are readily removed, allowing one to look directly into the module and see the separator-lens mask via the mirror. It is best, however, to remove the AF sensor chip from the module, to allow light to pass through the separator lenses and illuminate the mask outline.
With the AF sensor removed, and shining some light onto the back of the separator lens cluster, we can image the separator mask:
This mask is located 21mm behind the field lens, along the optical axis. The center group of four openings are for the cross-type AF points, which require four separator lenses. The outer pairs are for the lateral AF points, which only need two separator lenses each since they are uni-directional.
This mask directly determines the size, shape and locations of the "patches" on the main lens rear exit pupil, through which the AF sensor receives all of its light. The outer field lenses are partially prismatic, and aimed so that their mask openings are projected to the same place as the top and bottom mask openings of the center group.
Each mask opening is 1mm wide, point-to-point, and 0.60mm high. The oblong or "squished hexagonal" shape gives a little more area than a circular mask would, for a brighter image at the AF sensor. The center-to-center separation between each of the four pairs is 2.07mm. When these are projected by the field lens to the best-focus position of 106mm away, the net magnification is 5x and the area of the projected mask image at the main lens is about 12mm^2.
The separation between the pairs of mask openings is less than I had expected, and actually gives this AF module the capability of focusing with f/8 lenses. The D3 may have a wider separation, so that the images of the mask openings will take up the f/5.6 circle at the main lens exit pupil.
I did not remove the separator lenses or their mask from the AF module, but did take a photo of the separator lens cluster from the back side, which faces the AF sensor. Like the field lenses, the separator lenses are all molded as a single piece of clear plastic. Looking through the lenses, you can see the mask openings (out of focus). It appears that there would be room for a different mask to be used here, which has the openings spaced a little wider; that could potentially be the only difference between this module, and the D3 version.
The eight separator lenses project non-overlapping images onto the AF sensor. The size and shape of those images is set by the field-lens masks, and is scaled by the ratio of the separator-lens and field-lens focal lengths.
In this D300 AF module, the images projected onto the AF sensor are 1.88mm high by 1.16mm wide, for the central group of cross-type points. The images for the lateral groups are the same height, but have their unique shape.
The sensor's ceramic package includes a "shoulder" at each side, coplanar with the surface of the sensor die. These shoulders are seated against two projecting ridges on the AF housing, and fixed with epoxy. It is the AF housing alone, which sets the axial alignment of all of the optical components; there is no adjustment provided. The lateral and vertical alignment of the AF sensor must be done with the aid of a jig while the epoxy sets.
As is typical for AF systems which have a large, regular array of AF points, the AF detection lines are contiguous, rather than separate for each AF point. Here we see 22 "merged" vertical detection lines, and the 10 horizontal lines which are used only for the center group of cross-type points:
The actual detection lines are the narrow black rectangles; the white bars alongside them are metallization for associated circuitry. In fact, the surface of the AF detection lines is the optically darkest surface on the entire chip.
The sensor die measures 8.85mm wide by 6.92mm high. Each of the vertical detection lines is 2.08mm long by 0.12mm wide; the horizontal lines are 1.36mm long. Comparing these to the size of the images given above, we see that there is an extra 0.1mm of detector-line length at each end, to provide some alignment margin.
The partitioning of the long detector lines into individual areas for each AF point is done in firmware, with the origin locations stored in flash memory. This requires a calibration procedure at the factory, to determine the precise origins. These are important, not only for correct location of the AF points in the image, but also for focus accuracy. A number of D800 owners have learned what can happen, if this calibration is not performed correctly.
The next post will discuss the AF sensor in greater depth.
By superimposing a photo of the images projected by the separator lenses onto the AF sensor, with an photo of the AF sensor itself, we can see how the 8 separator images line up with the AF detection lines.
In this view, imagine that the sensor has become transparent, except for the detection lines which show in white, and that you are looking through the AF sensor from the back side:
We see three different images since each field lens and mask selects a different portion of the camera's image - for left group, center group and right group. Note that the left and right groups end up swapped to opposite sides of the sensor, thus the outermost 3 AF points from those groups fall on the innermost of their eight detection lines.
If the camera lens were correctly focused, the two images in each of the four pairs (three top/bottom pairs plus one left/right pair for center group) would be located in exactly the same place on their detection lines. Here, the lens is back-focused which causes each image pair to be spaced further apart; the AF system will respond by focusing the lens closer until the image pairs fall in the same place on their detection lines.
Detection Line Detail
The sensel structure in the detection lines is not visible, at least in the visual range of wavelengths. No matter how much I push exposure and enhance contrast in the sensor photos, I am unable to identify any periodic structures within the detection lines. However, we have some useful clues from the adjacent circuitry. Alongside each detector line, is a sequence of circuits which repeat at 6um intervals; this may correspond to the sensel pitch along the length of the line. This means that each vertical line would have 350 rows of sensels, and each horizontal line would have about 230.
Unlike image sensors, however, there is no need to have square sensels - they could have any aspect ratio. In fact, there is some advantage to rectangular sensels for the AF detection lines. Each detection line is 120um wide, and likely includes a number of columns of sensels - unfortunately we cannot see how many. If there were 10 columns, for example, each vertical detection line would have 3500 sensels total.
A second interesting detail, is that there is masking at each end of the lines, which has an angled edge. The skew of this edge is 15um along the length of the detection line. This suggests to me that the columns of sensels are staggered, to provide spatial resolution much finer than the 6um sensel size.
Here is a tight crop from the very center of the AF sensor, showing the details discussed above:
However, a 15um stagger doesn't fit very nicely with a 6um sensel pitch - it isn't a nice integer multiple. The actual size for the sensels remains a bit of a puzzle. I would like to invite comments from others who are more familiar with the details of IC design and may be able to deduce more from the above image.
Numbers for Focus Precision
The field lens masks are 8.4mm high, and the images projected by the separator lenses are 1.88mm high. This means the magnification at the AF sensor, relative to the main-lens image, is 1/4.5.
If we are using an f/8 lens on the camera (which matches the spread angle of the separator mask images "projected" by the field lens), the movement of the images on the detection lines will be 1/4.5 as much as the radius of the COC in the main image. For example, if the main lens is a little out of focus so that it produces a 20um-diameter (10um radius) COC in the main image, then the images on the AF sensor's detection lines will be displaced 10um/4.5 = 2.2um. We want the AF system to be able to detect a displacement of this size when an f/8 lens is in use.
For wider-aperture lenses, the requirement is much tighter. An f/1.4 lens will produce a COC diameter that is 5.6x larger, for the same image displacement at the detection lines; in other words the COC diameter would be 112um in the above case. To get this back down to a 20um COC or less (which is still a bit large for a sharp image on the D300), the AF sensor needs to be able to detect an image shift of only 0.4um on its detection lines.
To meet this tight spatial resolution, the detection lines would need to have at least 15 staggered columns of 6um sensels. If we allow main-image COC sizes up to 30um diameter, then the detection lines would need just 10 staggered columns of sensels producing 0.6um spatial resolution; I suspect this may have been the actual design aim for the D300 AF system when using f/1.4 or similar lenses.
First, a quick review of the D300 sensor and its associated separator mask for comparison. Here is the D300 sensor, which has two sets of vertical detection lines plus two sets of horizontal detection lines for the center group, and just two sets of vertical detection lines for each of the lateral groups:
Each of the eight sets of detection lines requires its own separator lens, so we find eight openings in the D300 separator-lens mask:
The Canon 1Dx design adds cross-type detection for two columns of AF points in each of the two lateral groups (with f/4 sensitivity horizontally), and f/2.8-sensitivity cross-type detection for the middle 5 AF points in the center column. This requires adding two sets of horizontal detection lines for each of the lateral groups of AF points, and four sets of detection lines to the center group. The detection lines for f/2.8 sensitivity need to be set about twice as far from center, as the f/5.6-sensitivity detection lines are. To minimize the AF sensor size, these have been set diagonally away from center, so the detection lines also need to run diagonally (photo released by Canon):
All of the additions require quite a bit more real estate, especially since the f/2.8-sensitivity lines for the center group require moving the three groups apart some. This sensor die measures about 15mm wide by 6.8mm high (note all dimensions are inferred from photos and may not be exact). To save a little space, the line sets for the lateral groups have been crowded a little closer; this requires the separator lenses for those groups to be slightly prismatic, to re-aim their rays closer together.
If you check dimensions carefully in this photo, you can see that the center-to-center spacing of the horizontal-line sets for the outer groups, is about 1.4x the center-to-center spacing of their vertical-line sets. This is because the outer cross-type AF points have f/4 sensitivity horizontally, but f/5.6-sensitivity vertically.
Another interesting detail, is the length of the detection lines for the f/2.8-sensitivity AF points (diagonal lines). These only serve a single AF point each, yet they are about as long as the horizontal lines for the center group, which each serve 3 AF points. This extra length is very useful for f/2.8 AF points, as otherwise the out-of-focus detection range would be very narrow.
I have not found any photos of the separator mask for this sensor, but have put together my own educated guess. The locations of the openings (relative spacings) should be fairly accurate, but the sizes and shapes of the openings are just my speculation (and I've used the D300 shapes for convenience). It's reasonable to expect that the mask openings for the f/4-sensitivity and f/2.8-sensitivity separator lenses will be larger since there is space on the main lens exit pupil for larger patches, further from center:
On the separator mask, the spacings between pairs of mask openings must all be exactly scaled to the size of the aperture circle on the main lens which they correspond to. Thus the openings for f/4-sensitivity are Sqrt(2) times further apart than the f/5.6-sensitivity openings, etc.
Here is a look at how the camera lens exit pupils are used by the D300 and EOS-1Dx AF systems. The D300 only uses (approximately) the f/8 circle, whereas the 1Dx uses the f/5.6, f/4 and f/2.8 circles. The 1Dx field lenses are aimed so that all six of the mask openings for vertical detection lines (f/5.6-sensitivity) come from exactly the same two patches on the main lens exit pupil. Also, the four f/4-sensitivity mask openings for the lateral-group horizontal lines will share two patches:
For perspective, I have shown aperture circles up to f/1.4. This underscores the baseline disadvantage for an AF system that is (nearly) restricted to using the f/8 circle.
Since the EOS-1Dx also uses 3 field lenses, the exterior appearance of the complete AF module is very similar to the D300/D3 module (photo released by Canon):
The sizes of the field-lens masks correspond to the sizes of the AF-point arrays for the three groups: Center array is 7 high by 3 wide and outer arrays are 5 high by 4 wide. Note that the field lens masks are unaffected by the design choice of AF-point sensitivity (f/5.6 vs f/4 vs f/2.8).
Here, the D300 AF module is set up with the 200 f/2 VR, looking at a subject about 7 feet away. The images projected onto the AF sensor are made visible by substituting a piece of matte transparent tape for the sensor. These were photographed by my D800E with a macro lens and exposure set to Manual.
A second camera was used to photograph the lens aperture from the front, to provide a means of measuring the f-stop setting. As a bonus, in these photos we can also see the separator mask openings projected onto the lens pupil.
The lens aperture lever was held by a cardboard wedge - first, near wide open (almost f/2), and second, stopped down to the point where one can just see some corner vignetting start to occur in the sensor images. The f-stop for the second case turns out to be about f/7.5, which is where the lens aperture diaphragm is just starting to cover the outer edge of one of the separator mask openings.
The primary result from this demonstration, is that the brightness of the images on the AF sensor is unchanged (other than the slight vignetting mentioned above). This demonstrates that none of the extra rays from opening the lens wider than f/7.5 are arriving at the AF sensor.
It is also interesting to note that with the lens wide open, there are some areas of flare occurring. With the lens stopped down, the flare is absent. In this composite, the left side shows the 200 f/2 front view when almost wide-open and the AF sensor images for that aperture; the right side shows the lens stopped down to about f/7.5 and the corresponding AF sensor images:
If the lens is stopped down beyond f/7.5, the AF sensor images very quickly fade to black as the lens diaphragm covers the separator-mask openings.
Today I replaced the "projection screen" on the D300 AF module, in an attempt to improve the visible image detail. Instead of frosty cellophane tape, I'm using a solid piece of clear plastic which I have filed on one side to produce a sort of "ground glass" surface. There is still quite a bit of texture visible, but I think it is possible to see more image detail now.
This demonstration will give the actual image shift in microns, for a change in lens focus. The setup is much the same as for my immediately preceding post: The 200 f/2 is aimed at a target about 7 ft. away, with the D300 AF module positioned behind it. The images projected by the separator lenses, onto the screen, are photographed by the D800E with a macro lens, at 1:1 magnification.
In the following composite, three examples of sensor images are shown (at 50% resolution). The first was taken with the lens focus ring set to the 8 ft. position. In this case, the separation between the separator-lens images in each pair, is 2.78mm.
The lens focus ring was then moved to the 7 ft. position for the second example. The separation between the images in each pair reduces to 2.70mm, a reduction of 80um, so each image has moved 40um (0.04mm) towards the other image in its pair.
For the third example, the lens focus was kept the same, but the lens was re-pointed slightly to the right. This demonstrates that all eight images move in the same direction when the subject moves, and the separation between the image pairs does not change.
The composite also includes a crop of the image taken by the camera through the 200 f/2. This crop shows the three areas which are selected by the field-lens mask; you will see that it is these three areas which are projected onto the AF sensor:
Looking carefully at these separator-lens images, you may notice that the focus has become slightly softer by changing the lens focus ring from the 8 ft. position to the 7 ft. position. This amount of defocus is considerably less than one sees in an image taken with the 200 f/2, even if it is set to f/8, when changing the focus ring between those two positions. In fact, the focus change seen here is very similar to what one sees in the camera image, if the 200 f/2 is set to f/22; this demonstrates the high depth of focus for the AF system, which is due to the small size of the patches on the main lens exit pupil that are used.
Calculated Image Shift
We can compare the 0.08mm shift in relative image positions, to the expected value that we calculate. When changing focus from 8 ft. (2438mm) to 7 ft. (2134mm), the 200 f/2 moves its image plane by 1/(1/200 - 1/2134) - 1/(1/200 - 1/2438) = 2.81mm along the optical axis. Since the AF system is using the f/8 circle, the lateral shift at the image sensor is 2.81mm/8 = 0.351mm. However, the D300 AF module scales the main image down by a factor of 4.5 for the AF sensor, so the shift seen at the AF sensor is 0.351mm/4.5 = 0.078mm, which compares well to the observed figure.
If you have read a few of my previous posts here, you are aware that the AF system is very selective about the light that it admits to the AF sensor, and only passes rays that come from the central f/5.6 or f/8 circle of the main lens. This means that when wider-aperture or "faster" lenses are used, there are quite a few extraneous rays shooting around inside the AF module.
We will take a look at what is happening inside the AF module housing, between the field lens array, and the separator-lens mask. To do this, I have removed the field lens array from the module housing, and set it up on a macro rail with an f/2 lens, and a screen placed exactly where the separator-lens mask would be (21mm behind the field lenses):
I photographed the field-lens projections at a number of different aperture settings of the main lens, from f/8 to f/2. In order to see the screen, the camera needed to be placed at a rather steep angle off-axis, so the photos are in perspective.
Recall that the field lens projects the main lens exit-pupil plane, onto the plane of the separator-lens mask, so we will see the shape of the lens diaphragm. In the first example, for f/8, the circles are outlining the areas where the separator-mask openings are; keep this in mind as a reference (I had wanted to place an actual-size copy of the separator mask on the screen, but decided that accurate alignment would have been too difficult).
As the main lens is opened wider, the field-lens projections become wider in proportion, until they achieve a wide overlap at f/2:
Of course, an f/1.4 lens would produce even larger circles. We see that the "fast" lenses would cause quite a problem, by mixing up light between the different field lenses.
To prevent this, and generally reduce flare from wide-aperture camera lenses, barrier walls are placed between the field-lens optical paths within the AF module housing:
Although the AF module is well-equipped with these internal black walls, they are not quite as non-reflective as some other surfaces, such as the inside of the camera's mirror box. Thus we can see noticeable flare from wide-aperture lenses (see prior post).
Let's take a close look at a photo I posted previously:
When setting up for this photo, it was extremely difficult to achieve precise alignment of the AF module, to the center of the main lens exit pupil. Here we can just start to see the effect of the residual misalignment, presenting as mild vignetting of the upper images at the AF sensor. For reasons I will discuss in more detail later, one does not want any discrepancies in the brightness of the two images in each pair, so this kind of off-center vignetting needs to be avoided as much as possible.
The angles that the separator-mask images make with the optical axis range from 2.0 deg. to 3.6 deg. (that range covers the radial width of the openings). In order for the images to remain well-centered in the lens aperture and avoid vignetting when the main lens is at - or even a little under - the minimum design aperture, the angular alignment of the AF module must be kept within a very small fraction of one degree.
To accomplish this (and also allow for fine-adjust of the AF module position along the optical axis), the module is suspended from its top frame by three fine-thread alignment screws which are spring-loaded:
The fine thread of the alignment screws provides movement of less than one micron, per degree of rotation. These adjustments are performed at the factory, and are interactive with the adjustment for the AF sub-mirror in the mirror box.
Unfortunately, many authors on the web have suggested use of the AF sub-mirror rest-stop adjustment as a means of global AF-error compensation. Changing the position of this stop throws the alignment of the viewfinder AF points out, and can result in loss of AF performance when the main lens is close to the AF-system minimum aperture (f/8 for the D300):
That small adjuster at the back of the mirror-box, just above the base, can only be set up correctly by running firmware on the camera that allows the AF-sensor images to be checked. If it is disturbed, there is no means for an owner to ensure that it is accurately returned to its original position.
As discussed in prior posts, the AF sensor has 11 pairs of vertical detection lines which serve all 51 AF points, and 5 pairs of horizontal detection lines for the central group of 15 cross-type sensors.
Each vertical detection line is 2.08mm long, but the image projected onto it is only 1.88mm high, leaving an alignment margin of 0.2mm total. Similarly, each horizontal detection line is 1.36mm long, but the image projected onto it is 1.16mm wide, again leaving 0.2mm of alignment margin. Both types of lines are 0.12mm wide.
Vertical lines are divided into 5 regions, for the 5 AF-point rows which use them. The spacing between these regions, i.e. their height, is precisely defined by the spacing between the horizontal detection lines (at least for the center group of 15 AF points), which is 0.36mm. The Horizontal lines are divided into 3 regions since they serve three columns of AF points in the center group. The spacing or width of these regions (defined by the spacing between vertical lines) is 0.38mm.
It is also worth mentioning that the spacing between the images projected onto the AF sensor by the separator lenses is slightly wider than the spacing between opposite groups of detection lines. This gives the images an outward shift of about 0.05mm on each side, rather than being precisely centered on the detection lines. I believe this is likely by design, rather than merely being a manufacturing tolerance; more about this later.
When the camera lens is in focus (and when using AF-S single-point AF), the horizontal and vertical spans where image detail is recognized for each AF point (i.e., where it is simultaneously visible on both left and right horizontal lines, or on both top and bottom vertical lines), is about 0.24mm wide or high. We now have a frame and dimensions for the individual AF-point regions, that we can use to discuss processing of the data taken from the detection lines. Here are the regions for the horizontal detection lines:
[Note: Relative positions of lines shown in this diagram is only for reasons of compactness, and does not reflect their physical layout on the sensor, where they are in fact co-linear and well separated.]
Establishing a Model
Not all details of the sensel layout on the detection lines are known at this point. It appears that they have a 6um pitch, but there is an unknown number of sensels across the 0.12mm width of the lines. It is also not known how the columns of sensels are staggered, and what spatial resolution results.
In order to continue the discussions, I have decided to use a simplified model of the detection-line sensel layout. The actual AF module will probably have better performance (precision and accuracy) than our model, so keep this in mind for the following discussions.
The model has a 6um sensel pitch, but each sensel is assumed to cover the full width of the line, so its dimensions will be 6um by 120um. Rectangular sensels such as this are likely used in a number of AF sensor designs. The data read from the detection lines is thus strictly one-dimensional; any image detail variations across the width of the line will be averaged out.
Each AF-point region on a horizontal detection line will include about 63 sensels, and on the vertical detection lines will include 60 sensels. The 0.24mm span within each AF point, containing image detail recognizable when the camera lens is at an in-focus position, will include 40 sensels; this is an important number and establishes the size of the data set used in calculating image correlations for focus-error determination.
The final assumption for our model, is that the range of data to be used when determining image shift from defocus, will be limited to the sensels within the selected AF point, plus only a few outside of that region. It is likely that the actual camera will go beyond this range in certain cases, although of course it will always be limited by the boundaries of the images projected onto the AF sensor.
Evaluating Image Shift
As has been shown in previous posts, the images projected onto the detection lines will move away from each other if the lens focus is moved toward infinity - or toward each other if the lens focus is moved closer. When the camera lens is in focus (barring any calibration modification such as AF fine-tune), the AF-point region on the left detection line will see exactly the same image details as the corresponding AF-point region on the right detection line does.
It is a very simple matter for us, with our visual cortex optimized for image recognition, to immediately determine the amount of image shift - which gives the direction and amount of the focus error.
The AF processor, however, must execute many steps to determine this, scanning the full range available within the AF point and checking for a match between the left and right image samples.
In our model, each step will require 40 value comparisons (one for each sensel in the 0.24mm span). To investigate the full width of the AF-point region (plus a bit), we will shift the test span in the left line from 13 sensels to the left of centered, to 13 sensels to the right of centered (the test span in the right line is moved in the opposite direction). For best resolution, we can shift the left and right test spans one at a time, giving a total of 53 steps to evaluate. For each step, we record a value which indicates how well the image samples within our test spans match.
Continued in next post . . .
The processing of data from the AF sensor starts with reading out the values from the detection lines. Here, I am limiting the discussion to a single AF point, which will be one of the central cross-type points equipped with both horizontal and vertical detection lines. We will work with the horizontal detection lines first.
Using our model as discussed previously, the detection-line sensels act to average out the detail across the 0.12mm width of the detection line. That is, the 2D image data is reduced to just one dimension.
As an example, I used some fairly small text which is only tall enough to span about half of the horizontal detection-line width; about 8 characters of the text fit into the AF-point box in the viewfinder. Comparing to the "quick brown fox" text in the previous post (which is really too fine for good AF), it would be about 2-3 times larger.
To simulate the function of the detection line, I photograph the text, then extract the average row data from the RAW file, using my image-analysis utility. The window for this extraction is 20 sensels high (corresponding to the 0.12mm detection-line width) and is 66 sensels long. This length includes enough sensels for the 40-sensel test span, plus another 13 sensels at each end to allow for that much shift. The 66 sensels take up about 0.40mm along the detection line (slightly more than the 0.38mm allotted to each AF point).
Due to the small size of the text, plus the fact that it only covers about half of the detection-line width, the contrast in the data from the detection lines is not very high. Here are plots of the 66 values from each line (left line in blue, right line in red):
At first glance, this tends to look like random noise, especially since the data come from two separate images which do not have the same sensel alignment to the image (causes some discrepancy in the fine shapes). If one takes a little time and looks closely, some matching features can be identified. (Hint: Shift the blue line to the right, and red line to the left, 8 positions.) This data will definitely pose a challenge for the AF processing to identify the shift.
Let's say that the values for the left line have been loaded into a 66-element array A and the values for the right line have been loaded into another 66-element array B residing in the processor's memory. We refer to the individual values as A to A and B to B.
Performing the Correlation
Thanks to details provided earlier by Bernard Delley from a Nikon patent, we can apply the same correlation approach specified by Nikon. The test span used by our model is 40 sensels wide, so we will take 40 contiguous data values at a time from the left line, and compare them to 40 contiguous data values from the right line.
The criterion used for comparison is simply the absolute value of the difference between sensel values. For each step in the process, we calculate the 40 absolute differences, then add them together; this sum is the correlation value for each step. When all steps are complete, we can plot the correlation values as a function of the test-span shifts that we used.
First step looks at the first 40 values in the A line and compares them to the last 40 values in the B line; that is, we are taking A-line values starting with a 13-sensel left shift from center, and taking B-line values starting with a 13-sensel right shift from center. The first correlation value is thus
C(-13) = Abs(A - B) + Abs(A - B) + . . . + Abs(A - B)
The next one will be
C(-12) = Abs(A - B) + Abs(A - B) + . . . + Abs(A - B)
Note that as the A indices go up, the B indices go down; our test spans are moving in opposite directions (toward each other, to start). When we have completed half the steps, the test spans will both be in the center; after that they will move apart again. The last step will be:
C(13) = Abs(A - B) + Abs(A - B) + . . . + Abs(A - B)
We can also "squeeze in" an intermediate step between each of the above 27 steps, if we only change one of the indices (instead of both) at a time. This improves spatial resolution, and gives us a total of 53 correlation values to use. I call these intermediate values C(-12.5), C(-11.5), etc.
The C() values that we compute will be large if the image samples in the test spans do not match, and will be small if the image samples in the test spans have a good match. When we plot the C() values, we are looking for the place on the curve that is lowest.
I created a spreadsheet which does all of the above correlation calculations, from the line data extracted by the image-analysis utility. Without further ado, here is the correlation curve for the line data shown in the plot above:
We see that the best match is at C(-8). This means that the 40-value window of Left line data, taken 8 sensels left of centered, matches the 40-value window of Right line data, taken 8 sensels to the right of centered. We conclude that the camera lens is out of focus, such that each image is 8 sensels = 48um away from its in-focus reference position. The autofocus system will respond by moving the lens focus closer until the images match with no shift. If we repeated the correlation-curve plot afterward, we would see the minimum value in the curve lands at 0 shift.
This is actually a difficult example, and the correlation curve indication is rather weak. We can also have a look at the vertical-line data and correlation, which will be much clearer.
For the vertical-line example, we still have a horizontal line of text running through the AF point as before, but there is also a horizontal line a little distance below it. This gives the vertical detection lines two strong features to detect. For this case, I have reversed the shifts (simulating front-focusing of the camera lens). Here are the plots of the values read from the vertical detection lines:
The wide troughs correspond to where the line of text is, and the narrow ones are from the horizontal line in the image.
Not surprisingly, the correlation plot gives us a much more definite indication:
This is what we like to see for a subject that allows accurate AF. The only feature that threatens to make the conclusion less clear, is the falloff at C(-13) and C(-12). This is due to the weak match found, between the text and the horizontal line in the image.
In the following posts, we will take a look at some cases that are potentially problematic, and also look at how well the AF system handles blur (such as diffraction blur) and soft subjects.
Following some experiments that I've been performing this week with my D3s AF system, there are clearly some capabilities that could not be achieved with a simple one-dimensional AF detection line that is the basis of my original model.
To improve representation of the real system, I have decided to upgrade my model to simulate a two-dimensional array of sensels in the detection line, with staggered columns as suggested by the slanted end-masking seen in the AF sensor photos.
The mask stagger is 15um total across the 120um width of the detection lines. There is still a question of how many columns of sensels lay within that 120um width; I have chosen a number of 5 for the model because it is a good compromise between complexity and convenience of collecting data for the model. This gives a shift of 3um for each column of sensels (a possible direct match to the real detection lines), and if we use the earlier approach of shifting just one test span at a time when performing the calculations, the spatial resolution achieved will be 1.5um.
The model corresponds to detection lines with sensels that are 24um wide and 15um high (referring to vertical detection lines). The region on the lines that corresponds to each AF point will use an array of sensels that is 5 wide by about 25 high. For performing correlation calculations, the size of the test span will be 16 sensels high, and we will shift it 6 sensels in each direction; the calculations thus will cover a total span of 28 sensels which extends just a bit outside the region for each AF point.
The calculations are performed for each of the 5 columns of sensels independently. That is, each is treated as a separate detection line with regard to correlations, because each column covers different detail. The correlation results are then combined by a moving window which takes 5 values at a time (one from each column) and this yields a total of 121 points on the final correlation plot.
Pros and Cons of the 2D detection line
The approach of using wide staggered sensels, instead of very narrow single sensels, works well for detail at most alignments (angles), but loses the advantage of the stagger in the case where image lines are angled to follow the stagger. In fact, this kind of rotational alignment is one parameter that I will be investigating later. The behavior, though, is often better than the one-dimensional line with narrow sensels, which quickly loses contrast for image lines at most angles.
The large size of the sensels is an advantage for light gathering and signal/noise ratio. However, it can also make very fine details produce rather low-amplitude contrast, i.e., weak signals for the correlation calculations to use.
The original model was intended to be used by taking image samples from the AF module's "screen" that I have installed in place of the AF sensor, so I was only using a 20x66 pixel strip from the camera image. This of course is extremely tiny and results in low resolution, as well as susceptibility to the texture of the AF module screen.
For the 2D model, I am taking image data from a direct camera image instead, selecting an area which corresponds to the AF detection line region for the AF point in use. Using the D800E, this is an image strip of 110x420 pixels, which is then divided into 140 individual-sensel areas. The extraction procedure is more complex, but has been automated to make it practical. It has the advantage that defocus and diffraction effects can be directly set for study when required, not to mention the convenience of being able to use any RAW image file to provide samples.
Following posts will generally make use of the 2D model, but there is one example using images directly from the AF module screen that I would like to present; it will use the 1D model to illustrate a particular AF system susceptibility.
As photographers, we like to find contrasty, well-defined edges for our cameras to focus on. It's natural to think that the AF system works best with such subjects, and that it would have difficulty focusing accurately with very soft edges.
But is this really true? If we think about how the correlation works - matching two image samples point-by-point - it should be able to match image samples that have gradual contrast transitions, as well as sharp ones. After all, it's digitizing the tones to resolution that should be sensitive to very small differences. A mismatch at gradual transitions will not produce large absolute-difference terms, but then there will be a relatively large number of terms that contribute.
In this example, I've run the 2D model on an image of decorative printing on a pillow, with the image focused well at f/16, and then defocused significantly. On the left is a plot of the detection line values, and on the right, the result plot for the correlation runs. Transitions are sharp for the in-focus case, but much smoother and more gradual in the defocused case. However, the correlation plots are almost indistinguishable, with just a small drop in amplitude for the defocused case:
This is actually an important capability, and demonstrates how the AF system is able to accurately compute focus error when the camera lens is far out of focus and the detail available to the AF sensor is quite blurred. This also covers the relatively small amount of blur caused by diffraction - even with the AF system's very "slow" aperture of about f/28 with respect to diffraction effects.
One may wonder how much blur the AF system can work with. Being the curious sort, I ran some experiments with my D3s, and then discovered a surprising result. As long as the subject contrast included within the selected AF point is high enough, blurred edges allow the camera to lock focus fairly easily; this is in line with expectations, knowing how the correlation works. However, if I used a soft edge with limited contrast range, AF was not possible.
There must be some processing of the detection-line data, to remove constant bias, and even compensate for gradual falloff in the image, across the AF point. This would be high-pass filtering, so that there is effectively an upper limit to the size of detail that can be used for focusing.
This would make sense, to prevent problems when the AF-sensor images start to vignette as can happen when lenses close to the minimum f/8 speed are used. Such vignetting would produce a tonal falloff in the images projected onto the AF sensor, which runs in opposite directions for the two images in each pair.
For example, on the vertical detection lines, the upper image would darken more at the top and the lower image would darken more at the bottom. This creates a mismatch between the images, which could swamp the image details we want the correlation calculations to find - especially if the subject does not have high contrast.
I ran some simulations of this, using the 1D model. Even given a subject with good contrast, I found that adding some tonal falloff (running opposite directions on the opposite detection lines) and image-brightness discrepancy can significantly degrade the correlation plot. Here is an example which uses the same test image that I used in some earlier posts, taken directly from the AF module screen. The upper plot is the original one, without any image vignetting, and the lower plot is the result after some vignetting and bias has been artificially introduced into the data:
The upper curve is clearly indicating the focus shift, but the lower curve has been distorted and has a second trough that could result in complete mis-focus, if the image contrast had been a little lower. Even the original trough at +5 has been shifted slightly to the right, which would reduce focus accuracy. High-pass filtering of the detection-line data will prevent these problems.
In an upcoming thread which investigates AF system capabilities and limits, I will revisit the topic of focusing on soft subjects.
Regular repeating patterns present one of the most common problems for phase-detect AF, and can cause severe mis-focus. Often, they will present the AF system with several choices for focus, all of which appear to be valid according to the correlation plot.
Here is an example, with the image data extracted from a photo of a ribbed knit band that has very consistent spacing between the ribs:
This correlation plot will give the camera four good choices to select from. The overwhelming tendency is for the AF system to choose the one that has lowest shift, i.e., the nearest choice. The photographer can guide the camera to the desired focus by pre-focusing manually before engaging AF. Because the troughs are deep and narrow, the camera is able to achieve very precise focus lock, i.e., the presence of the alternative focus choices does not degrade focus accuracy for the selected option.
Fortunately, only subtle departures from regularity in the pattern can give the camera enough information to select the "correct" focus without manual guidance from the operator. In the next example, slight shading near the center of the pattern gives it an overall contour which improves the correlation plot. There are only two good choices remaining for the camera to select from; in actual operation with this subject, there was a very strong tendency to select the "correct" option, and the alternate was only chosen if the lens was pre-focused all the way down to its minimum focus distance:
Minor Details Provide Major Assistance
Some subjects may contain strong repeating patterns, but include enough small irregular detail to allow the camera to find focus very dependably. In the next example (see inset), a bar-code pattern has four heavy black bars which are almost evenly spaced, and the overall pattern is almost symmetrical, but the correlation plot shows that correct focus will be easily achieved:
To Summarize - Focusing on Regular Patterns
Manual pre-focus provides good guidance for the AF system to select desired focus.
When AF is guided to select the desired alternative, focus precision is typically very high.
Relatively minor irregular features can provide adequate guidance for the AF system to select correct focus and reject alternative focus positions.
What is the finest detail that the AF system can detect?
Due to its very "slow" aperture - about f/28 with regard to diffraction effects - the AF system's optical resolution limit is primarily set by diffraction.
Coming up with a good figure for the Airy disc size is not quite straightforward, due to the odd shape of the area on the camera-lens exit pupil which the AF system takes its light from:
We can start by calculating the Airy disc size for a circular aperture with the same diameter as the minor diameter of the hex-shaped apertures. This is 3.0mm, at a distance of 106mm from the field lens, giving us f/35. The Airy disc diameter for a circular aperture will be 47um.
Due to the rather straight sides and extra width of the AF-system apertures, we can justifiably take out the 1.22x correction factor that is used for circular apertures, giving an Airy disc diameter of 39um. The shape of the Airy disc will not be quite circular; the wide aperture shapes will reduce the diameter of the Airy "disc" somewhat in the tangential direction. Since we are interested in the extent of the Airy disc along the length of the AF detection lines, though, we want to use the larger 39um figure.
The 39um Airy diameter at the field lens is reduced by the low magnification of the separator lenses, to slightly less than 9um at the AF sensor chip. Since there are some additional small contributions to diffraction from the separator lenses, we will take 9um as the effective size.
To give the calculations a more precise meaning, let us assume that as a test subject, we are using 50/50 white/black bars such as are typically used for lens resolution tests. We need to compute the effect of diffraction on the contrast of such bars. This is not straightforward, but can be readily evaluated by using my Vcam application. I calculate percent contrast as 100 * (Max - Min)/(Max + Min) where Max and Min are the highest and lowest tonal values in the projected image, as given by Vcam.
Let T be the spatial period of the white/black bars, i.e., the total width of one white bar plus one black bar, which is also called one "cycle." Let Da be the diameter of the Airy disc. Contrast is then determined strictly by the ratio of Da/T; as Da increases relative to T, contrast decreases. When Da becomes large enough relative to T (or T becomes small enough relative to Da), all detail in the projected bars is completely lost, i.e. contrast goes precisely to zero and the projected image is a flat medium gray.
This behavior is universal to all sorts of optical testing, so the figures provided below are very useful in estimating diffraction effects when they dominate resolution in lens testing (the ratios have funny values since they follow some common apertures for a particular case):
2.55 or higher
Since our Da value is 9um, we see that having T at 7um would give us 50% contrast, or having T at about 4.5um would give us 15% contrast. The latter is commonly taken as lowest-acceptable contrast in optical systems.
If the detection-line design follows the assumption used for the 2D model, the combined spatial resolution of the sensels is 3um, which would be the widest sampling period that one wants to have for signal periods down to T=6um. Thus we see that the detection-line spatial resolution matches very nicely with a point on the contrast curve where there is still good usable contrast; the system should be able to "see" test bars at periods around 6um, across a wide range of lighting.
Experiments with my D3s verify that this is about the limit of the AF system. To put this into perspective for a user, this corresponds to having about 40 line pairs within the height of the AF-point box in the viewfinder display, or about 55 line pairs across the width of the AF-point box. Under bright lighting, this may improve slightly, but the extinction limit occurs at about 65 line pairs vertically or 90 line pairs horizontally within the AF-point box, and this limit can only be approached - never fully achieved.
With today's AF systems rated down to about LV -2, I thought it would be a good idea to take a look at the amount of light available to the AF sensor at such low illuminations.
I will take a two-step approach which first estimates the photon flux available to the D300 imaging sensor, then calculate the gain scaling relative to that, to arrive at the photon flux for the AF sensels.
The camera's meter will be used as a reference, not because this is the most accurate approach, but because of its practicality to photographers. We then take our definition of LV -2 to be that light level which produces a nominal exposure reading when the camera has been set to ISO 1600, f/2.8 and 2 sec exposure time; this is equivalent to ISO 100, f/1 and 4 sec.
By taking measurements from the RAW file under the above conditions, then compensating for the sensor QE figure (per sensorgen.info), we find that there is a flux of about 400 photons per second to each D300 green-channel imager sensel. Since this is after the color filter, we need to compensate for filter loss, giving a conservative estimate of 500 photons per second without the filter.
The AF system has the field-lens mask positioned typically 106mm behind the main lens exit pupil, and at this distance, it takes light from a small patch of the main lens exit pupil that is 12.5 square mm. All of the light from this patch that passes through the field-lens mask, ends up within an image area at the AF sensor which is 1.88mm high by 1.16mm wide. This area (taking the sensel size of 24um by 15um as used in the 2D model discussed previously) is equivalent to 6060 AF sensels, so if we call the total light flux (from the main-lens patch that is collected by the field lens) T (photons/sec), then each AF sensel receives T/6060. However, in the camera this is reduced by the beam-splitter mirror; if we take an estimate of 35% for transmission through the mirror, each AF sensel will receive T/17300.
For the main image sensor, let's start with the same 12.5 square mm patch on the lens exit pupil. The image sensor is around 6mm closer to the lens, than the AF system's field lenses, so taking the light projection angle that matches the field lens size, the photon flux T will be shared by some 1.26 million D300 imager sensels (corresponding imager area is 7.9mm by 4.8mm). Now we scale up according to the exit-pupil size of an f/2.8 lens, which is 80x the area of the patch used by the AF system: Each D300 imager sensel receives a photon flux of T/15700.
Finally, taking the ratio of AF-sensel flux to imager-sensel flux for the above case, we have (T/17300)/(T/15700) which is 91%. That is, each AF sensel receives 91% as much photon flux as the imager sensels do, when the latter are operating behind an f/2.8 lens.
From the estimate given above, at LV -2 with an f/2.8 lens, there is a flux of 500 photons per second arriving at each imager sensel, so we expect a flux of about 450 photons/sec for each AF sensel. [Note that although we "used" an f/2.8 lens for the calculations, we could just as well have used other apertures, and would still arrive at the figure of 450 photons/sec for the AF sensels.]
The D300 is capable of 8 frames/sec, so the upper limit for integration time in the AF system may be only as much as 60msec. At 450 photons/sec, this means each AF sensel will only receive 27 photons at LV -2. Allowing for quantum efficiency, the signal/noise ratio considering just shot noise would be only about 4.5.
In the presence of such rather high noise levels, we can appreciate that subjects at LV -2 need good contrast, so that noise will not swamp the signal available for the correlation calculations.