Testing the linearity of a CMOS image sensor

Question

The EMVA 1288 standard guides how to measure the linearity of a digital image sensor, i.e., if the digital number from a pixel changes linearly to the incident light intensity. The procedure includes a measurement of the incident light intensity, which requires a separate light detector from the image sensor. However, I thought that one can simply determine the linearity by fixing the light intensity and all other settings and by adjusting the exposure time. If the pixel response is linear with respect to the exposure time, the all of the conversions (1)-(4) should be linear. Am I missing something?

(1) conversion of photons to photoelectrons

(2) conversion of photoelectrons to a voltage (by a capacitor)

(3) amplification of the voltage

(4) conversion of the voltage to a digital number

Answer 1

This could work if the exposure time is linear, but it may not be, it depends on how the gating of the timer works. But in the end you'll be testing the linearity of exposure timing and how well that works. I would think that you would want that variable to be fixed and adjust the actual photons going into the device instead of changing how you measure the photons.

Answer 2

I do not think that measuring linearity with respect to exposure time is the same as linearity with respect to intensity. For intensity, a photodetector will start to saturate and behave non-linearly as its voltage output approaches the bias voltage, which depends on the applied voltage and the load resistance (see these experiments from Thorlabs). As for exposure time, the linearity will depend on the quantizer which will saturate when it reaches its maximum integer size.

This is to say, you can saturate the detector at any exposure time with a sufficiently intense light source (e.g. pointing a strong laser right at the detector). Or you can saturate the ADC by applying a certain intensity, which may or may not be in the detector's linear range, for an amount of time that causes it to count up to its max value. I don't believe that there is an equivalency between these two things.

Answer 3

You're asking for the photon transfer curve. Janesick's book Photon transfer : DN --> [lambda] is the goto reference source for this. Search for photon transfer curve

Answer 4

However, I thought that one can simply determine the linearity by fixing the light intensity and all other settings and by adjusting the exposure time. If the pixel response is linear with respect to the exposure time, all of the conversions (1)-(4) should be linear. Am I missing something?

This is actually one of the methods described by the standard:

6.3 Variation of Irradiation
Basically, there are three possibilities to vary the radiant exposure of the sensor, i. e., the
radiation energy per area received by the image sensor:

I. Constant illumination with variable exposure time.
With this method, the light source is operated with constant radiance and the radiant
exposure is changed by the variation of the exposure time. The radiant exposure H
is given as the irradiance E times the exposure time texp of the camera. Because the
dark signal generally may depend on the exposure time, it is required to measure the
dark image at every exposure time used. The absolute calibration depends on the true
exposure time being equal to the exposure time set in the camera

https://www.emva.org/wp-content/uploads/EMVA1288Linear_4.0Release.pdf

So yes, that is a valid method in so much as you know the exposure time accurately, which is probably the case so long as the exposure times are relatively long and thus not seriously affected by quantization of clock cycles. Note that you will still need some means of calibration (of DN to photons) to get absolute linearity (relative to number of photons).