optimized some text

joss/paper.md

@@ -44,7 +44,7 @@ Developed using a Python 3 stack, `PAOS` is released under the BSD 3-Clau
 
 <!-- A summary of the results of the benchmarking tests. -->
 
-We benchmarked `PAOS` against `PROPER` [@Krist:2007] on the HST optical system, because `PROPER` is not designed to handle `Ariel`’s, which i) is off-axis and ii) involves more complex elements than simple thin lenses, such as dichroics. The description of the HST system used is the one provided in the `Hubble_simple.py` file in the `PROPER` package[^1]. This description was translated into an input file[^2] for `PAOS` for reproducibility. All simulation inputs have been matched (e.g., wavelength, grid size, `zoom`[^3]). We added a line in the `PROPER` HST routine to set the pixel subsampling factor used to antialias the edges of shapes. We set this value to 101 from the default 11 to more closely match the exact treatment given in `PAOS`.
+We benchmarked `PAOS` against `PROPER` [@Krist:2007] on the HST optical system, because `PROPER` is not designed to handle a more complex optical system such as `Ariel`’s, which i) is off-axis and ii) involves other elements than simple thin lenses (e.g.&thinsp;dichroics). The description of the HST system used is the one provided in the `Hubble_simple.py` file in the `PROPER` package[^1]. This description was translated into an input file[^2] for `PAOS`. All simulation inputs have been matched (e.g., wavelength, grid size, `zoom`[^3]). We added a line in the `PROPER` HST routine to set the pixel subsampling factor used to antialias the edges of shapes. We set this value to 101 from the default 11 to more closely match the exact treatment given in `PAOS`.
 
 We compared the resulting PSFs at the focal plane of the telescope, both in the central region and in the outer wings. The first benchmark is reported below, showing the results for the PSFs at 1 $\mu$m. \autoref{fig:benchmark-1} shows the central region of the HST PSFs as computed with `PAOS` and `PROPER`, and their difference. No significant residuals were found, with sporadic outlier pixels showing deviations by < 0.1 dB in regions corresponding to the PSF zeros due to small numerical errors.
 
@@ -54,7 +54,7 @@ We compared the resulting PSFs at the focal plane of the telescope, both in the
 
 ![Comparison between PSF slices along the x and y axis, respectively. The left column reports the slice values for both codes, whilst the right column reports their difference. The units are the same (power per pixel in dB) to highlight even the smallest discrepancies. As can be observed, these differences are negligible for powers $\gtrsim$-50 dB for the HST application. \label{fig:benchmark-2}](hubble_psf_comparison.pdf){height=100%}
 
-\autoref{fig:benchmark-aberrated-1} and \ref{fig:benchmark-aberrated-2} report the second benchmark; in this case, we simulate an aberrated PSF by HST described by a superposition of Zernike polynomials. At M2, we added 100 nm RMS (WFE) each for defocus, vertical astigmatism, and oblique astigmatism, totaling $\sigma \approx$ 173.2 nm WFE. The simulation is performed at $\lambda$ = 1.0 $\mu$m; therefore, using the Ruze formula [@Ross:2009], the Strehl ratio is $S = \exp\left(- 2 \pi \sigma / \lambda \right)\approx$ 0.3. Consequently, the PSF is highly aberrated and the main lobe is spread over more pixels. Thus, we can validate the `PAOS` implementation of optical aberrations, and we have a larger region of high signal. The latter is especially useful for investigating aliasing errors, which tend to occur more severely where the distribution has the highest amplitude because the amplitudes of the signal and the error add rather than the intensities [@Lawrence:1992].
+\autoref{fig:benchmark-aberrated-1} and \ref{fig:benchmark-aberrated-2} report the second benchmark; in this case, we simulate an aberrated HST PSF, where the wavefront error (WFE) is described by a superposition of Zernike polynomials. At M2, we added 100 nm RMS (WFE) each for defocus, vertical astigmatism, and oblique astigmatism, totaling $\sigma \approx$ 173.2 nm WFE. The simulation is performed at $\lambda$ = 1.0 $\mu$m; therefore, using the Ruze formula [@Ross:2009], the Strehl ratio is $S = \exp\left(- 2 \pi \sigma / \lambda \right)\approx$ 0.3. Consequently, the PSF is highly aberrated and the main lobe is spread over more pixels. Thus, we can validate the `PAOS` implementation of optical aberrations, and we have a larger region of high signal. The latter is especially useful for investigating aliasing errors, which tend to occur more severely where the distribution has the highest amplitude because the amplitudes of the signal and the error add rather than the intensities [@Lawrence:1992].
 
 ![Same as \autoref{fig:benchmark-1}, but adding an optical aberration using Zernike polynomials: 100 nm RMS (WFE) for each of three low-order coefficients in the Zernike expansion: defocus and primary astigmatism (vertical and oblique), corresponding to the coefficients 4, 5, and 6 in the Noll ordering, respectively. The difference between the large-scale features of the PSFs is negligible. \label{fig:benchmark-aberrated-1}](hubble_psf2d_comparison_aberrated.pdf){height=100%}
 
@@ -65,7 +65,7 @@ We find that the differences between the aberrated PSFs are negligible and reach
 In summary, we find that `PAOS` is a robust and reliable tool for simulating the propagation of optical wavefronts through complex optical systems, as shown by the excellent agreement with the results obtained with `PROPER` for HST in our benchmark tests.
 
 [^1]: The `PROPER` source code and documentation can be downloaded at <https://proper-library.sourceforge.net/>.
-[^2]: `Hubble_simple.ini`, included in the package under the `lens data` directory.
+[^2]: `Hubble_simple.ini`, included in the package under the `lens data` directory for reproducibility.
 [^3]: The ratio between the grid's linear dimension and the beam size at the initial surface.
 
 # Statement of need