Optics shift invariant

• Optical image scripts and tutorials
• Zernike polynomials
• Wavefront implementation

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Background

Many ISETCam calculations use a shift-invariant optical calculation. Shift invariance means that the image created by a point in the scene is spread by the same amount in the image, no matter the position of the point in the scene. In ISETCam this image, called the point spread function (PSF), depends on the wavelength of the point. In optics the image region over which shift-invariance is a good approximation for a given lens is called its isoplanatic region.

The shift-invariant approximation is appropriate for a subset of conditions. In general the point spread function depends on where the point is in the scene and, most importantly, the distance to the point. But the approximation makes is very useful for many scenes, for example when scenes with a modest (20 deg) field of view and with all the objects at approximately the same distance (in a plane). It is also useful when all the objects are sufficiently far away, because for most lenses the PSF does not change much beyond a certain distance. This distance depends on the lens, but for the human eye or for the classical double Gauss lens, the distance is 10-20 focal lengths.

Wavefronts

Wavefront aberrations are described using the international standard Zernike polynomial representations, which includes aberrations with specific labels such as defocus, coma, and different types of astigmatism.

In the spectral irradiance calculations, wavefront aberrations are converted into a point spread function. The PSF is convolved with the spectral radiance. The implementation requires paying attention to the details of the sampling rate for the scene spectral radiance. There are many tutorials and examples of these calculations in the ISETCam toolbox.

Diffraction limited

The diffraction-limited calculation is based on the formula for a diffraction-limited, circular aperture. The calculation is shift-invariant, applying the classic point spread uniformly across the scene to create the optical image. The point spread is wavelength-dependent, but shift-invariant.

The diffraction-limited PSF depends only on the f-number of the lens. We will explain the formula and the issues with spatial sampling here.

We will contrast this calculation with the wavefront calculation, which can also be diffraction limited. They differ in how they handle the spatial sampling. The wavefront calculation,which is a bit slower, is more accurate for very high dynamic range scenes.

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