prysm.x.shack_hartmann#

Shack-Hartmann phase screens.

prysm.x.shack_hartmann.shack_hartmann(pitch, n, efl, wavelength, x, y, aperture=<function rectangle>, aperture_kwargs=None, shift=False)#

Create the complex screen for a shack hartmann lenslet array.

Parameters:

  • pitch (float) – lenslet pitch, mm

  • n (int or tuple of (int, int)) – number of lenslets

  • efl (float) – focal length of each lenslet, mm

  • wavelength (float) – wavelength of light, microns

  • x (numpy.ndarray) – x coordinates that define the space of the lens, mm

  • y (numpy.ndarray) – y coordinates that define the space of the beam, mm

  • aperture (callable, optional) – the aperture can either be: f(lenslet_semidiameter, x=x, y=y, **kwargs) or f(lenslet_semidiameter, r=r, **kwargs) typically, it will be either prysm.geometry.circle or prysm.geometry.rectangle

  • aperture_kwargs (dict, optional) – the keyword arguments for the aperture function, if any

  • shift (bool, optional) – if True, shift the lenslet array by half a pitch in the +x/+y directions

Returns:

complex ndarray, such that: wf2 = wf * shack_hartmann_complex_screen(… efl=efl) wf3 = wf2.free_space(efl=efl) wf3 represents the complex E-field at the detector, you are likely

interested in wf3.intensity

Return type:

numpy.ndarray

Notes

There are many subtle constraints when simulating Shack-Hartmann sensors: 1) there must be enough samples across a lenslet to avoid aliasing the phase screen

i.e., (2pi i / wvl)(r^2 / 2f) evolves slowly; implying that somewhat larger F/# lenslets are easier to sample well, or relatively large arrays are required. For low-order aberrations at the input in moderate amplitudes, >= 32 samples per lenslet is OK, although 64 to 128 or more samples per lenslet should be used for beams containing high order aberrations in any meaningful quantity. For a 64x64 lenslet array, the lower bound of 32 samples per lenslet = 2048 array

2) there must be dense enough sampling in the output plane to well sample each point spready function, i.e. dx <= (lambda*fno_lenslet)/2 3) the F/# of the lenslet must be _small_ enough that the lenslets’ point spread functions only minimally overlap