Sensor Analysis Primer –
Engineering and Photographic Dynamic Range

Prepared 2009-03-02 by Bill Claff Last revised 2017-05-16

### Introduction

Engineering and Photographic Dynamic Range (PDR) can be read
directly from a close relative to the Photon Transfer Curve (PTC).

### The Photon Transfer Curve with a Twist

Here is a chart of the Photon
Transfer Curve for the Nikon D300 in ADUs at all whole ISOs based on 14-bit
ADUs:

Note that for simplicity I am only showing the Gr channel
from the Color Filter Array (CFA).

In this variation the y-axis is Signal to Noise Ratio (SNR)
rather than the noise.

In my mind this is the single most important chart that
characterized the performance of any sensor.

The data can be use to compute both Engineering and
Photographic Dynamic Range.

### Engineering Dynamic Range

The low endpoint for Engineering Dynamic Range is determined
by where the SNR curve crosses the value of 1.

Here is an extreme close-up of that area of the Photon
Transfer Curve:

The ISO 100 line crosses 0 (the log_{2}(1)) at 1.63
EV.

So Engineering Dynamic Range is 14.00 EV – 1.63 EV = 12.37
EV.

Or, if we use the White Level (from White
Level), (14.00 EV – 0.11 EV) – 1.63 EV = 12.26 EV.

### Photographic Dynamic Range

My definition of Photographic Dynamic Range is a low
endpoint with an SNR of 20 when adjusted for the appropriate Circle Of
Confusion (COC) for the sensor.

For the D300 the SNR values on this curve is for a 5.5
micron square photosite.

To correct for a COC of .022mm we are looking for a log_{2}
SNR value of 2.49.

Here is an close-up of the area of the curve:

Note that the ISO 100 crosses 2.49 at 5.00 EV.

So Photographic Dynamic Range at ISO 100 is 14.00 EV – 5.00
EV = 9.00 EV.

Or, if we use the White Level (from White
Level), (14.00 EV – 0.11 EV) – 5.00 EV = 8.89 EV.

### Conclusions

Both Engineering and Photographic Dynamic Ranges computed in
this article are slightly higher than those I report elsewhere.

The reason is that this analysis is because we only used the
Gr channel from the Color Filter Array (CFA) and my reported values are across
all channels.

Since the red and blue channels perform a little less well,
the average across channels is lower.

Although the chart in terms of ADUs is of the most practical
use it is important to remember the lessons learned in examining the
electron-based Photon Transfer Curve.

As gain (ISO) is raised, fewer electrons are gathered; so in
actuality it is the highlights that are lost.

When the data is shifted to recover the lost highlights then
noise becomes apparent in the shadows.