final editorial comment

paper.md

@@ -49,7 +49,7 @@ Empirical PSF characterization tools like Point Spread Function Extractor (PSFEx
 `ShOpt` bridges the speed of `PSFex` with the features of `PIFF` using fewer configurable hyperparameters. `ShOpt` employs a number of techniques to optimize the speed of the program. First and foremost, `ShOpt` is equipped with support for multithreading. Polynomial interpolation is used for handling PSF variations across the field of view. The polynomials given to each basis element of the PSF are independent of one another and therefore can be distributed to different CPU threads to be run in parallel. `ShOpt` also introduces new methods for fitting both analytic profiles and pixel based profiles. If an analytic profile is used to model the PSF, then there are $3$ basis elements parameterizing the model. We choose 2D elliptical Gaussians for these analytic profiles because they are cheap to compute. Moreover, we use the Limited Memory Broyden–Fletcher–Goldfarb–Shanno algorithm (LBFGS) to find these paramters. This is faster but more memory intensive than Conjugate Gradient, the algorithm used in `PIFF`. Moreover, the $3$ basis elements are constrained to the manifold $B_2(r) \times \mathbb{R}_+$, where $B_2(r) = \{ (x,y) : x^2 + y^2 < 1 \}$ and $\mathbb{R}_+ = \{ x : x > 0 \}$. We constructed a function that maps any point in $\mathbb{R}^3$ into $B_2(r) \times \mathbb{R}_+$. The LBFGS algorithm uses successive iterations to converge to a solution for the $3$ basis elements, and so we use this function to ensure that our update steps in LBFGS do not leave the constraint. For the pixel basis, both `PIFF` and `PSFex` approximate the PSF by minimizing the reduced $\chi^2$ between a grid of pixels and a star vignette. PCA can quickly achieve the same purpose of approximating the input vignette without overfitting to background noise. We also provide an autoencoder mode, which uses deep learning to reconstruct the image. The weights and biases are not reset between stars, so the knowledge of how to reconstruct one star is transfered to the next. This in turn leads to fewer training iterations. Finally, `ShOpt` is written in Julia. Julia uses a just in time compiler which makes it faster than intepreted languages such as Python and has shown to be a good choice for performance critical code [@Stanitzki_2021]. 
 
 # State of the Field
-The JWST captures images at high resolution and at wavelengths of light that have been previously unexplored [@Gardner_2006]. With these images we are seeing farther into the early universe than we ever have before. The complex optics of JWST coupled with our desire to get the most out of the incredible data have presented the community with new set of challenges that current software does not address: the need to create high-fidelity models of the point spread function for diffraction-limited images across a wide range of wavelengths. ShOpt.jl is one attempt do solve this challenge and other teams are approaching the issue in complementary ways, as described below.
+The JWST captures images at high resolution and at wavelengths of light that have been previously unexplored [@Gardner_2006]. With these images we are seeing farther into the early universe than we ever have before. The complex optics of JWST coupled with our desire to get the most out of the incredible data have presented the community with new set of challenges that current software does not address: the need to create high-fidelity models of the point spread function for diffraction-limited images across a wide range of wavelengths. `ShOpt.jl` is one attempt to solve this challenge and other teams are approaching the issue in complementary ways, as described below.
 
 A number of JWST PSF libraries already exist, using both empirical and forward-modeling approaches. We describe them here and draw attention to their strengths and weaknesses to further motivate the development of `ShOpt.jl`. As described in the statement of need, `PSFex` was one of the first precise and general purpose tools used for empirical PSF fitting. However, the Dark Energy Survey collaboration reported small but noticeable discrepancies between the sizes of `PSFex` models and the sizes of observed stars. They also reported ripple-like patterns in the spatial variation of star-PSF residuals across the field of view [@Jarvis_2020], which they attributed to the astrometric distortion solutions for the Dark Energy Camera.