What optical systems are we talking about? Some lenses/mirrors included in the sample scanner which images something (like laser light)? What about the spectrometer?

Assuming it's the former case with lenses/mirrors:

You can either assume diffraction limited components and calculate your spectral response (point spread function / modulation transfer function) in matlab from that, knowing about fourier pairs of different signals. (in my opinion, this would be a good start)

If you also want to simulate optical aberrations you need a different approach. Here, optical raytracing software would be needed. You could export the above mentioned data. (but I think this would be overkill for a first step)

For the spectrometer: I'm not sure what you want to simulate here. A spectrometer does detect the spectral response of light, but regarding the wavelength, and not the spatial frequency used in image processing.

So, since I'm not familiar with your topic, my answer might not be what you were looking for, but this came to my mind reading your question.

Thank you a lot, Thorsten Zwinger . This supposingly is that what I want to do.

I have SD-OCT system consisting of SLD, simple fiber-based Michelson interferometer, scanner with objective and simple spectrometer (collimator, transmision difraction grating, focusing lens and CCD line array). Currently I am developing algorithms to extract sample depth profile from CCD signal. I am testing theese algorithms using simple model of OCT signal. I would like to take into account certain depth of field of the scanner, abberations and chromatic despersion (accross 60nm). It would also be great to incorporate model of the spectrometer (but probably this is overkill).

So to obtain a proper algorithm of extracting sample depth profile I am thinking to create a model of scanner to simulate depth of field and chromatic abberation.

Okay, I think I understood your goal.

Since I work as an optical engineer, I can say, that setting up such a complex system (esp. spectrometer) is by no means an easy task just to simulate a realistic CCD-data. But it's possible. A good commercial available software is Zemax OpticStudio/Ansys but it's expensive. It does have a matlab API though. I also heard about a python raytracing module, but I never used that.

(if you want realistic results, you need the optical design of your system, which includes lens thickness and distances, radii and glas types)

Thinking about a way to simplify it, my approach would be to get knowledge about the expected signal and translate that to a filter you can use by convolving it with your clean CCD signal. What you need is the point spread function or MTF which is basically the spatial transfer function of the system (of a point source which equals a dirac impulse). If you assume diffraction limits, you can calculate this function from arbitrary specifications of your system, but in real life, all aberrations are included in this transfer function.

Dispersion means different focii for different wavelengths, so your flat CCD detector would detect slightly unsharp images of your laser, depending on the wavelength dependant current focal point, which would be either in front of or behind your CCD. (lateral chromatic aberration)

I think you can convolve your signal with different low pass filters (the point spread function is a low pass filter). You can find an interesting webside here (which covers the physics of this stuff, but not the signal processing):

https://www.telescope-optics.net/diffraction_image.htm

So, all in all: What does a CCD do? It detects energy, which is the square of the physical signal amplitude (= PSF), so your digital signal can't be negative. In reality the CCD is placed at the best focus of the system, where you can maximize the resolution and detect the PSF in the best possible way.

But introducing lateral chromatic aberration means, your best focal point for a different wavelength doesn't match the current CCD position, which implies, that you can't detect the PSF in the best possible way. The CCD plane and the energy signal of the PSF intersect slightly before / behind the best position.

From this, you could *somehow* (I don't know how) create a slightly modified PSF which depicts a slightly unsharp image.

I also don't know if it wouldn't be easier to just run a low pass filter over your signal.

Good low pass filters can be derived from understand the PSF and the diffraction limit of an optical system. You don't have the aberrations included, but it would be a good start.

Many thanks to you, Thorsten Zwinger !