# Overview of POPPY (Physical Optics Propagation in Python)¶

POPPY, which stands for Physical Optics Propagation in Python, implements an object-oriented system for modeling physical optics propagation with diffraction, particularly for telescopic and coronagraphic imaging. (Right now only image and pupil planes are supported; intermediate planes are a future goal.)

Note

This is an abbreviated version of the documentation for POPPY, included here as a brief summary relevant for WebbPSF. For more comprehensive documentation for POPPY please see the full POPPY documentation

## Introduction¶

The POPPY functionality lives under the package name poppy, which is available separately from WebbPSF and contains general functionality for Fraunhofer domain optical simulation. WebbPSF uses POPPY under the hood to perform calculations, and indeed POPPY began its life as part of WebbPSF.

POPPY includes a system for modeling a complete instrument (including optical propagation, synthetic photometry, and pointing jitter), and a variety of useful utility functions for analysing and plotting PSFs, documented below.

Note

This code makes use of the python standard module logging for output information. Top-level details of the calculation are output at level logging.INFO, while details of the propagation through each optical plane are printed at level logging.DEBUG. See the Python logging documentation for an explanation of how to redirect the poppy logger to the screen, a textfile, or any other log destination of your choice.

## The Object-Oriented Optical Model¶

To model optical propagation, POPPY implements an object-oriented system for representing an optical train. There are a variety of OpticalElement classes representing both physical elements as apertures, mirrors, and apodizers, and also implicit operations on wavefronts, such as rotations or tilts. Each OpticalElement may be defined either via analytic functions (e.g. a simple circular aperture) or by numerical input FITS files (e.g. the complex JWST aperture with appropriate per-segment WFE). A series of such OpticalElements is chained together in order in an OpticalSystem class. That class is capable of generating Wavefronts (another class) suitable for propagation through the desired elements (with correct array size and sampling), and then performing the optical propagation onto the final image plane.

There is an even higher level class Instrument which adds support for selectable instrument mechanisms (such as filter wheels, pupil stops, etc). In particular it adds support for computing via synthetic photometry the appropriate weights for multiwavelength computations through a spectral bandpass filter, and for PSF blurring due to pointing jitter (neither of which effects are modeled by OpticalSystem). Given a specified instrument configuration, an appropriate OpticalSystem is generated, the appropriate wavelengths and weights are calculated based on the bandpass filter and target source spectrum, the PSF is calculated, and optionally is then convolved with a blurring kernel due to pointing jitter. All of the WebbPSF instruments are implemented by subclassing poppy.Instrument.

## Algorithms, Approximations, and Performance¶

POPPY presently assumes that optical propagation can be modeled using Fraunhofer diffraction (far-field), such that the relationship between pupil and image plane optics is given by two-dimensional Fourier transforms. Fresnel propagation is not currently supported.

Two different algorithmic flavors of Fourier transforms are used in POPPY. The familiar FFT algorithm is used for transformations between pupil and image planes in the general case. This algorithm is relatively fast (O(N log(N))) but imposes strict constraints on the relative sizes and samplings of pupil and image plane arrays. Obtaining fine sampling in the image plane requires very large oversized pupil plane arrays and vice versa, and image plane pixel sampling becomes wavelength dependent.

To avoid these constraints, for transforms onto the final Detector plane, instead a Matrix Fourier Transform (MFT) algorithm is used (See Soummer et al. 2007 Optics Express). This allows computation of the PSF directly on the desired detector pixel scale or an arbitrarily finely subsampled version therof. For equivalent array sizes N, the MFT is slower than the FFT (O(N^3)), but in practice the ability to freely choose a more appropriate N (and to avoid the need for post-FFT interpolation onto a common pixel scale) more than makes up for this and the MFT is faster.