How To Measure “Photon Transfer Curve” (2) ?

This blog will contain some further information on how to construct the Photon Transfer Curve, because it is possible to obtain the same information in various ways. What actually is needed for the PTC is a curve representing :

- the noise (standard deviation, variance, signal-to-noise ratio), versus,

- the sensor output signal (output signal, output signal corrected for offset or effective output signal), or,

- the sensor input signal (that was needed to generate the noise under consideration). Although none of the previous blogs did discuss this option, it is also a possible way to deduce the quantum efficiency by means of the PTC. This is the preferred way of using the PTC in the EMVA1288 standard. Unfortunately when measuring the input of the light level that goes to the sensor, one of the attractive features of the PTC is lost, being the fact that no absolute measurements of the light input is needed. For that reason here it is left out of the discussion.

To create a PTC curve the following options are available :

1) Grabbing images in dark : the dark current itself and the temporal noise measured in dark can be used to generate a PTC curve, although it would not be the first choice of doing ! But the dark current itself can be easily changed/modified and the noise can be very simply measured. Changing the dark current can be done by changing the exposure/integration time and/or by changing the temperature. Grabbing several images at the same setting (exposure time and temperature) can be used to calculate the temporal noise for each pixel. Averaging the obtained noise values and averaging the output signals can give rise to a single point on the PTC curve. Notice that more images and more pixels per image will lead to better results. In the case the noise distribution from pixel to pixel turns out to be too large, one can eliminate the outliers, or one can work with a smaller area instead of working with the complete sensor area. In principle the limited sensor area can be reduced to a single pixel, this is still enough to generate decent data for a PTC curve.

2) Grabbing images with uniform light input : the average output signal of a sensor under uniform illumination and the noise on pixel level can be easily calculated for a given integration time of the sensor. Also in this way a single point on the PTC curve can be obtained. It should be noted that the PTC curve is used to evaluate temporal noise and not non-uniformities of the light source. So special attention needs to be paid to the uniformity and stability of the light source. If a uniform light input over the total area of the sensor cannot be guaranteed, a reduced sensor area can be used to generate a PTC curve. In the extreme, one single pixel can be used to create the PTC curve.

3) Grabbing images with non-uniform light input : from the previous it can be learned that a single pixel can deliver the data for a PTC if the light intensity to this pixel is changed. On the opposite, if the light intensity across the various pixels of a sensor is changed, then each individual pixel can generate a particular point on the PTC curve. If one takes care that these pixels get a large variety of light input, then a complete PTC curve can be obtained. For example by means of :

a. Two sets of images, a first set with non-uniform light input and a second set with no light input. The second set is needed to generate a decent dark reference frame used to cancel the offset of every pixel. The first set is needed to generate the average signal as well as the temporal noise figure for every single pixel. It should be clear that the more images one gets in each set of images, the higher the accuracy will be of the PTC curve.

b. One set of images with a non-uniform light input and a single image in dark. In this case the single dark image can be used to compensate for the offset, but one should take into account that this dark frame is not noise free. Also in this case, a higher number of images in the first set will increase the accuracy of the PTC curve.

c. One set of images with a non-uniform light input. These are used to calculate the average output level and the temporal noise level of each pixel. In the case no dark reference frame is available, one can rely on the darkest area in the average output frame to define the offset. Although only an “educated” guess can be made of the offset, the accuracy of the PTC curve and the obtained results can be increased by grabbing as many as possible images.

In the training developed by Harvest Imaging, the construction of a Photon Transfer Curve gets a lot of attention.  It is amazing how low the number of input images/data needs to be to create a valuable evaluation tool for the camera or sensor.  For more information and exploration of the PTC method, you should attend one of the Harvest Imaging courses and say “Thank You” to Jim Janesick, who originally developed this technique.

Albert, 19-09-2012.

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