Improved Exponential Phase Mask for Generating Defocus Invariance of Wavefront Coding Systems

Round 1

Reviewer 1 Report

This is a theoretical paper describing a method to reduce the defocus aberration of optical systems by using a phase mask. The results showed the point spread function and in the modulation transfer function of the improved exponential phase mask. My main problem with the paper is that the phase mask is improved to reduce the defocus of wavefront coding optical system and from my understanding a wavefront coding is a code used for measuring the aberrations. Therefore, I was confused all the text. I will recommend to the authors to add to the introduction some basic explanations: What is a wavefront coding optical system? When and how one has to use a phase mask? i.e., an example of phase mask use. How can a phase mask reduce the o make invariant the defocus term? Some figures with drawing may help, but a short explanation in the introduction is enough. Also I propose the authors to include a Discussion section, different than conclusion, where the results of simulations and from theory are summarized.

Some other questions are:

• Can the phase mask be used with incoherent radiation?
• Line 29: … designing a phase mask with a suitable shape to modify the optical system… Do the author mean to “modify the imaging of the optical system…” instead?
• Is the wavelength really only introduced in the phase difference but not in the surface equation of the phase mask?
• Is H (rho, phi) the OTF?
• Which units are used for the defocus term in the section 3?
• In Fig. 7a), phi=60 has a value half of the rest of phi. Looking the other phase masks looks like is quite normal that for this value the PSF decrease dramatically, but on the other hand means that for this value is very difficult to suppress the offset between peaks. Could the author comment on that?
• In Fig. 7a) the value of the PSF decrease from 0.4 to 0.35 compared with the other phase masks, except the cubic phase. The cubic phase mask is also used in the text as a reference of well supressed offset of peaks. Could the author comments if there is a relation between suppression of offset of peaks and decreasing the total value of PSF?
• 9 shows the defocus difference applied for different Phi values and phase mask type, however, is very difficult to find differences between the 9 images. I suggest magnification of the area of interest, use of a different figure or pointing at least the area of interest in the text.
• Line 250 says rusults instead of results
• Ref [2] Line 309: There is a mistype in the title of the article.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Jing Sheng et al. present an improved exponential phase mask in this contribution, which reduces the imaging position deviation introduced by the phase mask to the optical imaging system. They use Taylor expansion to construct the structure of the phase mask and fisher information for the optimization of the parameters. They compare the improved phase mask in a simulation benchmark to other stat of the art phase masks. They look at the MTF-Variation, the defocusing PSF curves and at an image simulation. Before a publication of the work in applied sciences can be recommended, there must be some revisions from the authors:

In the stat of the art description, the Jacobi-Fourier phase masks are missing. Here is a publication of the phase masks: https://0-www-sciencedirect-com.brum.beds.ac.uk/science/article/pii/S0143816618316956 this should be added.

The simulation chain for the imaging process should be described more clearly. How are the simulated images in figure 9 generated? How many pixel were used? What is the sampling? What is the f-number of the simulated optical system? Was noise added in the simulation? What is the signal to noise ratio?  In addition, the description of the figure 9 is missing. It should be clear which row is which phase mask topology.

Author Response

Thank you for your advice on our manuscript. The reply of your suggestions is as follows.

1、In the stat of the art description, the Jacobi-Fourier phase masks are missing. Here is a publication of the phase masks:

https://0-www-sciencedirect-com.brum.beds.ac.uk/science/article/pii/S0143816618316956 this should be added.

Answer: Thank you for your advice. I have added the Jacobi-Fourier phase mask in the introduction part.

2、The simulation chain for the imaging process should be described more clearly. How are the simulated images in figure 9 generated? How many pixel were used? What is the sampling? What is the f-number of the simulated optical system? Was noise added in the simulation? What is the signal to noise ratio?  In addition, the description of the figure 9 is missing. It should be clear which row is which phase mask topology.

Answer: We calculate the 2D-PSF of the system in MATLAB, and downsample it to a  template. The “Image man” has a size of . We use this PSF to convolve the original image and add Gaussian noise with a variance of 0.0001 to this image to simulate the optical imaging result from the wavefront coding optical system. And then we use the Wiener filter to restore this image to get the final imaging result as figure 9 shows. The f-number hasn’t been considered in this simulation, because we mainly want to discuss the effects of defocus. Gaussian noise with a variance of 0.0001 has been added in the simulation, and the SNR is 80dB. We add the description of figure 9.

Round 2

Reviewer 2 Report

The authors answered the questions. I can now recommend its publication.