Fresnel Propagation

POPPY now includes support for Fresnel propagation as well as Fraunhofer. Particular credit is due to Ewan Douglas for initially developing this code. This substantial upgrade to poppy enables calculation of wavefronts propagated arbitrary distances in free space, for applications such as Gaussian beam propagation and modeling of Talbot effect mixing between phase and amplitude aberrations.

Caution

The Fresnel code has been cross-checked against the PROPER library by John Krist to verify accuracy and correctness of output. A test suite is provided along with poppy in the tests subdirectory and users are encouraged to run these tests themselves. However this is still a relatively new addition to poppy, and it is possible there may still be some bugs.

Usage of the Fresnel code

The API has been kept as similar as possible to the original Fraunhofer mode of poppy. There are FresnelWavefront and FresnelOpticalSystem classes, which can be used for the most part similar to the Wavefront and OpticalSystem classes.

Users are encouraged to consult the Jupyter notebook Fresnel_Propagation_Demo for examples of how to use the Fresnel code.

Key Differences from Fraunhofer mode

The Fresnel propagation API necessarily differs in several ways from the original Fraunhofer API in poppy. Let’s highlight a few of the key differences. First, when we define a Fresnel wavefront, the first argument specifies the desired diameter of the wavefront, and must be given as an astropy.Quantity of dimension length:

import astropy.units as u
wf_fresnel = poppy.FresnelWavefront(0.5*u.m,wavelength=2200e-9,npix=npix,oversample=4)
# versus:
wf_fraunhofer = poppy.Wavefront(diam=0.5, wavelength=2200e-9,npix=npix,oversample=4)

The Fresnel code relies on the Quantity framework to enforce consistent units and dimensionality. You can use any desired unit of length, from nanometers to parsecs and beyond, and the code will convert units appropriately. This also shows up when requesting an optical propagation. Rather than having implicit transformations between pupil and image planes, for Fresnel propagation a specific distance must be given. This too is a Quantity giving a length.

wf.propagate_fresnel(5*u.km)

The parameters of a Gaussian beam may be modified (making it converging or diverging) by adding optical power. In poppy this is represented with the QuadraticLens class. This is so named because it applies a purely quadratic phase term, i.e. representative of a parabolic mirror or a lens considered in the paraxial approximation. Right now, only the Fresnel QuadraticLens class will actually cause the Gaussian beam parameters to change. You won’t get that effect by adding wavefront error with some other OpticalElement class.

Just like the OpticalSystem serves as a high-level container for OpticalElements in Fraunhofer propagation, the FresnelOpticalSystem serves the same purpose in Fresnel propagation. Note that when adding OpticalElements to the FresnelOpticalSystem, you use an add_optic function and must specify a physical distance separating that optic from the previous optic, again as an astropy.Quantity of dimension length. This replaces the addImage and addPupil methods used in Fraunhofer propagation.

For more details and examples of code usage, consult the Jupyter notebook Fresnel_Propagation_Demo.

A worked example of a compound microscope in POPPY is available here, reproducing the microscope example case provided in the PROPER manual.

References

The following references were helpful in the development of this code.