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Spectral Quantum Efficiency of some unmodified Nikon DSLR

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Bernard Delley:
With the pending closure of dpreview, I repost one of my more substantial threads in shortened, more concise form here.
The original post was on the Photographic Science and Technology forum, May 7, 2019.
I really liked the threaded form there, with indentations clearly showing which previous post got commented.

I have been curious about the QE of sensors since some time and have occasionally posted on QE and on spectral response too.  The approach to derive the number of electrons in a pixel, based on Poisson statistics, is well known on this forum. The crux for getting actual ISO or QE, was to measure the light incident on the sensor. My ages old Lunasix exposure meter can do incident (ambient) light measurements. It is an analog device with a reading accuracy of about 1/6 of a stop or so, that means about +-10% accuracy.  I recently realized that with the XRite i1Studio on gets a photo-spectrometer in the amateur  price range.  As a digital device it can be expected to be 10x more accurate than the old analog device. I could not find specs though, confirming my supposed calibration accuracy at the 1% level.  The subtleties in calibration are expected more at the level of angular sensitivity: approximately Lambertian.  With such equipment it should be easy, right ?

One prepares an illuminated slit and places a transmission grating in front of the lens, and the camera has been transformed in a spectrometer itself to measure its photo-response.

To calibrate it, one improvises a dummy camera, and takes the photo-spectrometer to measure the incident photon flux at the sensor position.

here is a result for some Nikon cameras:
Quantum efficiency: Number of electrons per photon incident on the pixel area. Number is peak efficiency in % for each type of pixel.

Bernard Delley:
Here is my measurement setup, to make an Interchangeable Lens Camera measure its own RGB spectral responses of its sensor assembly.

The sensor, lens and grating form a rigid assembly. I use a footed lens, so different cameras with the same mount can be tested in the same geometry. A special case it an old analog camera with the same F-mount which is used to place the photometer at the sensor position to measure the incident photon flux.  The lens is set at its 200mm mark. But this lens has FL 160mm when focused at the virtual spectrum object, which is approximately at the same distance as the slit, about 2.6 m.   The reproduction ratio is about 1:14 .  When the camera remains positioned within 1mm with respect to the slit, the spectral  image location remains within 1 nm.

With the transmission grating 500 lines/mm above arrangement produces a linear spectrum in the wavelength with a better than 1 nm accuracy even with a typical moderate amount of pincushion distortion by the lens. the geometry is to put 550nm at the center, the 400 nm end of the spectrum goes off 12mm to the indicated side of the sensor and the 700mm end 12 mm to the other side, so it just fits the Nikon DX format.The Lens is used wide open at f/2.8, but the 35mm slide format of the grating provides an aperture more like f/5.6 .  No significant vignetting was seen with this external aperture.

Bernard Delley:
calibration of wavelength

For the arrangement shown in the previous scheme, a 500 lines/mm grid leads to wavelength deviations shown below. The grid is fixed parallel to the sensor and the camera axis points such that 550 nm in the -1 order diffraction falls to the center of the sensor as shown in the scheme.

The effect of the grid & beam geometry alone leads to the blue curve. With a lens having a known pincushion distortion of 0.65% over the DX field, the brown line deviation function results. (A lens with barrel distortion of -0.28% would lead to a perfect compensation of wavelength deviations on the scale of this figure)

Nikon sensors available to me all show prominently an edge in the blue and one in the red response curve. This is used for auto-calibration in my software, and the wavelenghts are linearly interpolated from there: this is shown as the skew gray calibration curve. The deviations between grey and brown remain well under 1 nm across the 400-700 nm spectral range.

The setup allows to shine laser pointers through the light diffusor and slit. Available lasers are violet "405nm" green "532nm" red "650nm". A typical record after a single auto-calibration looks like this when checked several times with the lasers.

The first green line width is bloated because of over exposure. The red line is off by 6-7 nm. Wikipedia says " The least expensive laser pointers use a deep-red laser diode near the 650 nm wavelength" .   A simple measurement of the lasers in a basic setup with the laser, grating and "white screen", retractable rule and no other components ,  strongly suggests that 405 and 532 lines may be accurate, but the red is more like 656 nm than its nominal 650.

Bernard Delley:
Calibration of photon flux at the sensor position using the ambient light function of the XRite i1 Studio photo spectrometer.

This is measured as a function of position along the spectrum. A function p(x,lambda) [mW/m^2/nm] to be converted to n(x,lambda) [photons/mum^2/nm/s] . The crux is that the photo-spectro-meter has a relatively large aperture. And because the flux is not that intense, I cannot reduce the aperture very much by an auxiliary slit aperture. So for now, I know p(x,lambda) with steps in x better than 1 mm and a resolution of 68 nm in lambda. Since all three factors below are expected to be spectrally broad featured this limitation it not a fail. Knowing that the real distribution p or n is much sharper in lambda, like 8 nm, helps to infer the relevant photon flux n(x,lambda) onto the pixel.

Below is the function p(x,lambda) and its envelope as measured by the XRite i1Studio photo-spectrometer along the sensor position in the dummy camera. The position along x is implicit in the centers of gravity of the positional spectra from the spectroscopic relation x(lambda) . The envelope (purple) + aperture width  is input to calibrate out the product of factors : spectral output of the light source, grating transmission, lens transmission.

Bernard Delley:
Calibration of digital raw number to electrons in a pixel has been posted long ago by Emil Martinec.
An analysis of this type for a D7100, which I posted in 2013 may serve as an example.

Noise analysis for raw file, D7100 at ISO 100 over 200x200 central pixels for overcast sky, with white paper diffusor in front of lens. In later experiments, I used the Mac white screen right in front of the lens, as no bad consequences of time dependence of this light source became a problem. And the spectral details are also not important for this.
The purple line model includes photon shot noise + read noise. The grey line model includes in addition photo response non-uniformity. Results: "camera gain" defined by Martinec as electrons per Digital raw Number unit, here 2.30 . Read noise 2.0 electrons RMS, Full Well capacity 36500, Response non-uniformity 0.0025=0.25% .

 

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