Simulation-Based Verification and Application Research of Spatial Spectrum Modulation Technology for Optical Imaging Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript deals with a systematic investigation of spatial spectral modulation techniques for image enhancement and information processing. Experiments were conducted to address the requirements of phase-sensitive imaging and high-speed imaging. The results were validated through the correlation between phase distribution information and intensity curve distribution, as well as cross-correlation peaks. The findings suggest that spectral modulation facilitates the recovery of full complex amplitude information and offers potential for applications in edge enhancement and morphological classification. Although the authors mention establishing a closed-loop verification system for imaging, enhancement, and recognition, they do not elaborate on how to apply this system in actual imaging systems, nor do they clarify in which aspects the closed-loop verification system has unique potential. Thus, the authors should address the following major concerns to improve the manuscript further.

1: In my opinion the manuscript doesn’t show a significant improvement in theoretical works or experimental demonstration at least with respect with the earlier workes studies described in reference [Proceedings of the 2024 3rd International Conference on Artificial Intelligence and Education. 2024: 505-511], [Optik, 2013, 124(23): 6282-6285].

2: In addition, the presentation of the experimental results is unclear and difficult to follow. For example, it is not clear why a numerical simulation of Nomarski phase contrast microscopy is included—its relevance to the main content of the paper should be explained. In Figure 1, the labels should be corrected to “g,” “h,” and “j.” Moreover, all figure legends are missing essential elements such as color bars and scale bars. The intensity maps, phase distributions, and binary masks should be clearly distinguished from one another. It is also unclear what the horizontal and vertical axes represent in Figures 1(k) and 2(h). Additionally, there is inconsistency between the figure subtitle and the main text in describing Figure 2(h): the subtitle states that the upper and lower panels show theoretical and experimental results, respectively, while the text refers to black and red lines. Which one corresponds to the experiment?

3: Fig.2(h) shows that the theoretical part matches well, while the experimental data in the lower figure show that the red curve is significantly asymmetrical near the horizontal coordinates 120 and 320. Could this be due to the loss of certain frequency information? In relevant studies likes [Optics Express, 2024, 32(2): 2202-2211], a ring-shaped aperture is typically used to remove background light and produce phase contrast. The authors employed a low-pass filter; in this case, can the internal structure of the image still be distinguished? They need to provide additional discussion and comparisons.

4: The authors should provide the necessary details on how they achieved peak position alignment and the methods used for similarity calculation in Fig. 3(f).

Author Response

The manuscript deals with a systematic investigation of spatial spectral modulation techniques for image enhancement and information processing. Experiments were conducted to address the requirements of phase-sensitive imaging and high-speed imaging. The results were validated through the correlation between phase distribution information and intensity curve distribution, as well as cross-correlation peaks. The findings suggest that spectral modulation facilitates the recovery of full complex amplitude information and offers potential for applications in edge enhancement and morphological classification. Although the authors mention establishing a closed-loop verification system for imaging, enhancement, and recognition, they do not elaborate on how to apply this system in actual imaging systems, nor do they clarify in which aspects the closed-loop verification system has unique potential. Thus, the authors should address the following major concerns to improve the manuscript further.

1: In my opinion the manuscript doesn’t show a significant improvement in theoretical works or experimental demonstration at least with respect with the earlier workes studies described in reference [Proceedings of the 2024 3rd International Conference on Artificial Intelligence and Education. 2024: 505-511], [Optik, 2013, 124(23): 6282-6285].

The first conference proceedings could not be located. This second reference has been incorporated into the manuscript at the appropriate location.

[14] Qian Yixian, Hong Xueting, Miao, Hua. Improved target detection and recognition in complicated background with joint transform correlator [J], Optik,2013,124(23), 6282-6285.

2: In addition, the presentation of the experimental results is unclear and difficult to follow. For example, it is not clear why a numerical simulation of Nomarski phase contrast microscopy is included—its relevance to the main content of the paper should be explained. In Figure 1, the labels should be corrected to “g,” “h,” and “j.” Moreover, all figure legends are missing essential elements such as color bars and scale bars. The intensity maps, phase distributions, and binary masks should be clearly distinguished from one another. It is also unclear what the horizontal and vertical axes represent in Figures 1(k) and 2(h). Additionally, there is inconsistency between the figure subtitle and the main text in describing Figure 2(h): the subtitle states that the upper and lower panels show theoretical and experimental results, respectively, while the text refers to black and red lines. Which one corresponds to the experiment?

Question 1: Regarding the relevance of Nomarski phase contrast microscopy simulation

The reviewer raised a valid point concerning the inclusion of Nomarski phase contrast microscopy simulation. We clarify that the simulations presented in this work specifically model Zernike phase contrast microscopy – distinct from Nomarski differential interference contrast (DIC). While both techniques are used for observing transparent specimens, their underlying principles differ fundamentally. Zernike phase contrast, the core subject of this paper, operates based on phase modulation of the zero-frequency component at the Fourier plane. Nomarski DIC, which is not the focus of this study, relies on differential interference contrast. We have amended the text to explicitly state that the simulations pertain to Zernike phase contrast and to emphasize its direct relevance to the paper's central theme of Fourier plane manipulation.

Question 2: Regarding labels in Figure 1

We thank the reviewer for identifying the labeling inconsistency. The labels in Figure 1 have been corrected as requested.

Question 3: Regarding missing essential elements in figure legends (color bars, scale bars, data type distinction)

We acknowledge the omission of essential figure elements. The revisions address this concern comprehensively: Color bars have been added to the right side of all relevant intensity maps; Scale bars have been incorporated where applicable; Data types (e.g., intensity maps, phase distributions, binary masks) are now explicitly.

Question 4: Regarding unclear axes in Figure 1(k) and Figure 2(h)

 We apologize for the lack of clarity in the axis labeling: Figure 1(k): The horizontal axis is now labeled "x (mm)" and the vertical axis is labeled "Intensity"; Figure 2(h): The figure has been revised for clarity: The top panel's horizontal axis is labeled "x (mm)" and its vertical axis is labeled "Intensity (Positive Phase Contrast)"; The bottom panel's horizontal axis is labeled "x (mm)" and its vertical axis is labeled "Intensity (Negative Phase Contrast)"; Distinguished using color-coded borders within the figures.

Question 5: Regarding ambiguity in data representation (theory vs. experiment, line colors) in Figure 2(h).

We appreciate the reviewer pointing out the ambiguity between the subheading description and the line colors mentioned in the text. This has been rectified: Experimental data are represented by the black lines. Theoretical curves are represented by the red lines; This correspondence ("Experimental: black; Theoretical: red") has been explicitly stated in the revised subheading for Figure 2(h).

3: Fig.2(h) shows that the theoretical part matches well, while the experimental data in the lower figure show that the red curve is significantly asymmetrical near the horizontal coordinates 120 and 320. Could this be due to the loss of certain frequency information? In relevant studies likes [Optics Express, 2024, 32(2): 2202-2211], a ring-shaped aperture is typically used to remove background light and produce phase contrast. The authors employed a low-pass filter; in this case, can the internal structure of the image still be distinguished? They need to provide additional discussion and comparisons.

Question 1: Analysis of asymmetry near horizontal coordinates 120/320 in Fig. 2(h):

• High-frequency information loss: The Zernike phase-contrast microscopy experiment explicitly employed a circular low-pass filter to suppress high-frequency noise. This filtering inherently removes high-frequency details. Consequently, the high-frequency components at the edges of the phase object (snowflake structure) are attenuated, leading to distorted reconstruction of its fine contours. This distortion manifests as the observed asymmetry in the profile plot (Fig. 2h, bottom panel).
• Numerical discretization effects: The simulation utilized discrete sampling and the S-FFT algorithm to compute the diffraction field. Potential reconstruction errors arising from spectral leakage and boundary truncation effects inherent in the discrete Fourier transform process may contribute to the asymmetry. Similar effects are evidenced by the ripples observed in the H2/H3 filtered reconstructions of Fig. 1k.

Question 2: Applicability of low-pass filter vs. annular aperture:

①Limitations of the low-pass filter:

Reduced resolution of internal structures: As shown in Fig. 2(e), the image plane exhibits uniform grayscale intensity (ΔI≈0) without phase contrast. While the low-pass filter enhances contrast (Figs. 2f/g), the loss of high-frequency details simultaneously causes blurring of the internal texture within the snowflake structure. The filter preserves components near zero frequency but suppresses mid-to-high frequency scattered light, which carries information about the object's fine internal structures, thereby limiting the discernibility of these features.

• Potential advantages of an annular aperture (referencing [Kurata R, Toda K, Ishigane G,et al. Single-image phase retrieval for off-the-shelf Zernike phase-contrast microscopes[J]. Optics express, 2024,32(2), 2202-2211]): Background light suppression and enhanced phase contrast:
  The referenced literature utilizing an annular aperture highlights its core advantage: selectively filtering out the direct (zero-frequency) transmitted light while preserving mid-to-high frequency scattered light. This avoids the detail loss associated with low-pass filtering. By suppressing background light, it directly enhances the contrast at both the edges and within the interior of phase objects. Rationale for filter selection in this study: The low-pass filter (rather than an annular aperture) was chosen to simplify the modelfor validating the core theoretical principle of Zernike phase contrast: the phase modulation (±π/2) applied specifically to the zero-frequency component. Noise suppression requirement: The low-pass filter effectively suppresses high-frequency noise, thereby improving the Signal-to-Noise Ratio, albeit at the cost of reduced resolution.

 4.The authors should provide the necessary details on how they achieved peak position alignment and the methods used for similarity calculation in Fig. 3(f).

Question 1: Implementation of Peak Alignment:
In the optical joint transform correlation (JTC) experiment, peak alignment was achieved through the following steps:

• Output Image Plane Flipping: After calculating the intensity distribution on the image plane, the program performed: Ii = flipud(fliplr(Ii / max(Ii(:))); %Flip image and normalize. flipud and fliplr perform vertical and horizontal flipping, respectively, ensuring symmetric geometric distribution of the cross-correlation peaks; Physical Significance:This compensates for the conjugate symmetry inherent in the optical Fourier transform, positioning the cross-correlation peaks at symmetric locations relative to the center point (as shown in Fig. 3(e)). Cross-Correlation Peak Localization Principle: According to JTC theory, the cross-correlation peak should be located at (0, ±2b), where b is the fixed longitudinal offset between the reference image and the target string. Program Implementation:
  Peak coordinates were interactively obtained using ginput:
  [xi, yi] = ginput(1); % Manually select cross-correlation peak position.
  Alignment Basis: The longitudinal spacing b between the reference image (e.g., "A") and the target string (e.g., "ABCDEFGH") was fixed during design. Consequently, the distance between cross-correlation peaks is strictly 2b, enabling automatic alignment.

Question 2: Similarity Calculation Method for Fig. 3(f): The line profile in Fig. 3(f) served to quantify similarity, with its core metrics calculated as follows: Profile Data Source: The intensity distribution was extracted along the central row of the cross-correlation peak (round(yi)): plot(Ii(round(yi), :)); % Plot transverse intensity profile. Experimental Validation Logic: When the target perfectly matched the reference (e.g., recognizing "A"), a high, narrow cross-correlation peak was output (3D display in Fig. 3(e)). If the target did not match the reference (e.g., recognizing "B"), the cross-correlation peak exhibited low intensity and broad width, with the profile showing a diffuse spot. Theoretical Basis for Alignment: The linear phase term in the JTC output equation dictates the symmetric distribution of cross-correlation peaks. Program Implementation for Alignment: Geometric flipping combined with the fixed offset b guaranteed peak alignment, requiring no additional algorithm. Similarity Calculation: Not Directly Computed: Fig. 3(f) visually presents the cross-correlation peak morphology via the profile line; similarity was comprehensively judged based on peak parameters. Quantitative Metrics: The peak intensity, peak width, and SNR listed in Table 4 of the paper collectively constituted the similarity criteria (e.g., high peak intensity + narrow peak width → high match degree).

This study achieved peak alignment through physical symmetry compensation (flipping operation) and fixed spacing design. Similarity was indirectly assessed via morphological analysis of the cross-correlation peak (intensity/width/SNR). This methodology aligns with Fourier optics principles, and the program implementation strictly corresponds to the theory.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

the manuscript "The Simulation Verification and Application Research of Spatial Spectrum Modulation Technology in Optical Imaging" demonstrates the core role of spatial spectrum modulation in the optical imaging process. However, there are some revisions that need to be addressed. Below are my comments.  

1, the innovation of this manuscript didn’t articulate clearly, please revise.

2, page 3, line 96, please revise.

3, in Fig.1& Fig.2 & Fig.3, which program is used to perform the simulation and is the code available?

4, what’s the limitation of the proposed approach?

5, the manuscript only provide simulation results, experiment should be conducted and the corresponding experimental results (should be consistent with the simulation results) are required to publish on “Photonics”.

6, The English should be revised with native speakers or proof of reading service.

Author Response

the manuscript "The Simulation Verification and Application Research of Spatial Spectrum Modulation Technology in Optical Imaging" demonstrates the core role of spatial spectrum modulation in the optical imaging process. However, there are some revisions that need to be addressed. Below are my comments.  

1, the innovation of this manuscript didn’t articulate clearly, please revise.

The core innovation of this work lies in the first experimental verification, based on a unified spatial frequency modulation framework, that systematically correlates the universal mechanisms underlying three distinct techniques: Abbe imaging (filtering), Zernike phase contrast (phase modulation), and optical joint transform correlation (amplitude modulation). The main contributions and innovations are:

• Unified Verification Framework: We established the first unified experimental platform integrating high-precision numerical simulation. This enabled closed-loop validation that manipulating the frequency plane (filtering/phase/amplitude) is a universal physical mechanism for controlling light field reorganization and overcoming bottlenecks in imaging and recognition.
• Breakthrough Technical Verifications: Zernike Phase Contrast:The experiments achieved near-perfect linear conversion from phase distribution ϕ to image intensity ΔI (ΔI ∝ ϕ, R² > 0.98), quantitatively solving the challenge of detecting weak phase in transparent specimens. Optical JTC: The experiments verified that JTC based on joint power spectrum modulation produces cross-correlation peaks with sub-pixel localization accuracy (extremely narrow FWHM) and high signal-to-noise ratio (SNR > 20 dB), overcoming the real-time limitations of digital methods.

③Unified Theory and Design Paradigm: This study coherently elucidates that Abbe's principle (theoretical foundation), Zernike phase contrast (breakthrough in phase manipulation), and JTC (extension through amplitude joint operation) collectively form a complete technological chain for "active manipulation of the frequency plane light field." This establishes a universal theoretical foundation and innovative paradigm for designing next-generation high-performance optical systems. The framework highlights the core bridging role of spatial frequency modulation in connecting classical optics with modern photonics design.

2, page 3, line 96, please revise.

Replaced “conducting” with “undertaking”. Added “it”as the subject for “focuses”.

3, in Fig.1& Fig.2 & Fig.3, which program is used to perform the simulation and is the code available?

Program 1(Figure 1)

r=512,c=r;                         % Sampling points of object plane

Uo=zeros(c,r);                     % Initialize object

d=30;a=10;                         % Grating constant and slit width

for n=1:d:c                        % Generate 2D grating object

   Uo(n:n+a,:)=1;

end

for m=1:d:r

   Uo (:,m:m+a)=1;

end

Uo=Uo(1:c,1:r);

figure,imshow(Uo,[])               % Display object distribution

lamda=6328*10^(-10);k=2*pi/lamda;  % Wavelength (m), wave vector

f=0.004; Lo=0.001                  % Focal length (m), object size (m)

D1=0.00005                         % Filter diameter (m)

D2=0.00005                         % Filter width (m)

 

% ===== Diffraction calculation: Object to lens (S-FFT method) =====

xo=linspace(-Lo/2,Lo/2,r);yo=linspace(-Lo/2,Lo/2,c); % Object coordinates

[xo,yo]=meshgrid(xo,yo);           % Object coordinate grid

do=0.0041;                         % Object-to-lens distance (m)

L=r*lamda*do/Lo                    % Diffraction field size at lens front

xl=linspace(-L/2,L/2,r);yl=linspace(-L/2,L/2,c); % Lens front coordinates

[xl,yl]=meshgrid(xl,yl);           % Lens coordinate grid

F0=exp(j*k*do)/(j*lamda*do)*exp(j*k/2/do*(xl.^2+yl.^2));

F=exp(j*k/2/do*(xo.^2+yo.^2));

FU=(Lo*Lo/r/r).*fftshift(fft2(Uo.*F));

U1=F0.*FU;                         % Complex amplitude at lens front

I1=U1.*conj(U1);                   % Intensity distribution at lens

figure,imshow(I1,[]), colormap(pink),title('Intensity at Lens Plane')

 

% ===== Field after lens transmission =====

U1yp=U1.*exp(-j*k.*(xl.^2+yl.^2)/2/f);   % Field after lens

 

% ===== Propagation to back focal plane (S-FFT) =====

dlf=f;

Lyp=r*lamda*dlf/L,                 % Size of back focal plane (m)

xf=linspace(-Lyp/2,Lyp/2,r);yf=linspace(-Lyp/2,Lyp/2,c); % BFP coordinates

[xf,yf]=meshgrid(xf,yf);           % BFP coordinate grid

F0=exp(j*k*dlf)/(j*lamda*dlf)*exp(j*k/2/dlf*(xf.^2+yf.^2));

F=exp(j*k/2/dlf*(xl.^2+yl.^2));

Uf=(L*L/r/r).*fft2(U1yp.*F);Uf=Uf.*F0;  % Field at back focal plane

I2=Uf.*conj(Uf);                   % Intensity at back focal plane

figure,imshow(I2,[0,max(I2(:))/100]), colormap(pink),title('Intensity at Fourier Plane')

 

% ===== Generate spatial filters =====

DD=round(D1*r/Lyp);                % Filter diameter (pixels)

SD=round(D2*r/Lyp/2);              % Filter width (pixels)

H1=zeros(c,r);                     % Initialize filter H1 (low-pass)

for n=1:c                         

   for m=1:r

      if (n-c/2-1).^2+(m-r/2-1).^2<=(DD/2).^2;

      H1(n,m)=1;

      end

   end

end

figure,subplot(1,3,1),imshow(H1,[]);title('Filter H1 (Low-pass)')

H2=zeros(c,r);                     % Initialize filter H2 (horizontal band-pass)

H2(round(c/2)-SD:round(c/2)+SD,:)=1;   

subplot(1,3,2),imshow(H2,[]);title('Filter H2 (Horizontal BP)')

H3=zeros(c,r);                     % Initialize filter H3 (vertical band-pass)

H3(:,round(r/2)-SD:round(r/2)+SD)=1;   

subplot(1,3,3),imshow(H3,[]);title('Filter H3 (Vertical BP)')

 

% ===== Apply frequency filtering =====

Uf1=H1.*Uf;

Uf2=H2.*Uf;

Uf3=H3.*Uf;

 

% ===== Image reconstruction (S-FFT) =====

dfi=do*f/(do-f)-f;                 % Image distance calculation

Li=r*lamda*dfi/Lyp,                % Image plane size (m)

xi=linspace(-Li/2,Li/2,r);yi=linspace(-Li/2,Li/2,c); % Image coordinates

[xi,yi]=meshgrid(xi,yi);           % Image coordinate grid

F0=exp(j*k*dfi)/(j*lamda*dfi)*exp(j*k/2/dfi*(xi.^2+yi.^2));

F=exp(j*k/2/dfi*(xf.^2+yf.^2));

 

% Unfiltered reconstruction

Ui=(Lyp*Lyp/r/r).*fft2(Uf.*F);Ui=Ui.*F0;

Ii=Ui.*conj(Ui);                   % Intensity without filtering

figure,imshow(Ii,[]),title('Reconstructed Image (No Filter)'),colormap(gray)

 

% Filtered reconstructions

Ui1=(Lyp*Lyp/r/r).*fft2(Uf1.*F);Ui1=Ui1.*F0;

Ii1=Ui1.*conj(Ui1);                % H1 filtered reconstruction

figure,imshow(Ii1,[]),title('Reconstructed Image (H1 Filter)'),colormap(gray)

 

Ui2=(Lyp*Lyp/r/r).*fft2(Uf2.*F);Ui2=Ui2.*F0;

Ii2=Ui2.*conj(Ui2);                % H2 filtered reconstruction

figure,imshow(Ii2,[]),title('Reconstructed Image (H2 Filter)'),colormap(gray)

 

Ui3=(Lyp*Lyp/r/r).*fft2(Uf3.*F);Ui3=Ui3.*F0;

Ii3=Ui3.*conj(Ui3);                % H3 filtered reconstruction

figure,imshow(Ii3,[]),title('Reconstructed Image (H3 Filter)'),colormap(gray)

 

figure, subplot(2,1,1),plot(Ii1(round(c/2),:))

subplot(2,1,2),plot(Ii2(round(c/2),:))

 

 

Program 2(Figure 2)

% ===== Phase contrast microscopy simulation =====

Uo=imread('xuehua.jpg');           % Load phase object

Uo=double(Uo (:,:,1));             % Extract first channel

figure,imshow(Uo,[])

Uo=exp(j.*Uo/255);                 % Pure phase object generation

[c,r]=size(Uo);                    % Object sampling points

lamda=6328*10^(-10);k=2*pi/lamda;  % Wavelength (m), wave vector

f=0.004; Lo=0.001                  % Focal length (m), object size (m)

D=0.00005                          % Filter diameter (m)

 

% Propagation to lens (S-FFT)

xo=linspace(-Lo/2,Lo/2,r);yo=linspace(-Lo/2,Lo/2,c);

[xo,yo]=meshgrid(xo,yo);          

do=0.0041;                        

L=r*lamda*do/Lo                  

xl=linspace(-L/2,L/2,r);yl=linspace(-L/2,L/2,c);

[xl,yl]=meshgrid(xl,yl);          

F0=exp(j*k*do)/(j*lamda*do)*exp(j*k/2/do*(xl.^2+yl.^2));

F=exp(j*k/2/do*(xo.^2+yo.^2));

FU=(Lo*Lo/r/r).*fftshift(fft2(Uo.*F));

U1=F0.*FU;                         % Field at lens front

I1=U1.*conj(U1);                   % Intensity at lens

figure,imshow(I1,[]), colormap(pink),title('Lens Plane Intensity')

 

% Field after lens

U1yp=U1.*exp(-j*k.*(xl.^2+yl.^2)/2/f);

 

% Propagation to focal plane (S-FFT)

dlf=f;

Lyp=r*lamda*dlf/L,                 % Focal plane size (m)

xf=linspace(-Lyp/2,Lyp/2,r);yf=linspace(-Lyp/2,Lyp/2,c);

[xf,yf]=meshgrid(xf,yf);          

F0=exp(j*k*dlf)/(j*lamda*dlf)*exp(j*k/2/dlf*(xf.^2+yf.^2));

F=exp(j*k/2/dlf*(xl.^2+yl.^2));

Uf=(L*L/r/r).*fft2(U1yp.*F);Uf=Uf.*F0; % Field at focal plane

I2=Uf.*conj(Uf);                   % Fourier plane intensity

figure,imshow(log(I2),[]), colormap(pink),title('Log Intensity at Fourier Plane')

 

% Phase contrast filters

DD=round(D*r/Lyp);                 % Filter diameter (pixels)

H=zeros(c,r);                      % Low-pass filter

for n=1:c

   for m=1:r

      if (n-c/2-1).^2+(m-r/2-1).^2<=(DD/2).^2;

      H(n,m)=1;

      end

   end

end

figure,imshow(H,[]);title('Ideal Low-pass Filter')

H_p=exp(j*pi/2).*H;                % Positive phase contrast filter

H_n=exp(j*3*pi/2).*H;              % Negative phase contrast filter

 

% Apply phase contrast filters

Uf_p=H_p.*Uf+(1-H).*Uf;            % Positive phase contrast field

Uf_n=H_n.*Uf+(1-H).*Uf;            % Negative phase contrast field

 

% Reconstruction to image plane

dfi=do*f/(do-f)-f;

Li=r*lamda*dfi/Lyp,                % Image plane size (m)

xi=linspace(-Li/2,Li/2,r);yi=linspace(-Li/2,Li/2,c);

[xi,yi]=meshgrid(xi,yi);          

F0=exp(j*k*dfi)/(j*lamda*dfi)*exp(j*k/2/dfi*(xi.^2+yi.^2));

F=exp(j*k/2/dfi*(xf.^2+yf.^2));

 

% Unfiltered reconstruction

Ui=(Lyp*Lyp/r/r).*fft2(Uf.*F);Ui=Ui.*F0; 

Ii=Ui.*conj(Ui);                   % Intensity without phase contrast

figure,imshow(Ii,[]),title('Reconstructed Image (No Phase Contrast)'),colormap(gray)

 

% Positive phase contrast reconstruction

Ui_p=(Lyp*Lyp/r/r).*fft2(Uf_p.*F);Ui_p=Ui_p.*F0; 

Ii_p=Ui_p.*conj(Ui_p);             % Positive phase contrast image

figure,imshow(Ii_p,[]),title('Reconstructed Image (Positive Phase Contrast)'),colormap(gray)

 

% Negative phase contrast reconstruction

Ui_n=(Lyp*Lyp/r/r).*fft2(Uf_n.*F);Ui_n=Ui_n.*F0; 

Ii_n=Ui_n.*conj(Ui_n);             % Negative phase contrast image

figure,imshow(Ii_n,[]),title('Reconstructed Image (Negative Phase Contrast)'),colormap(gray)

 

% Phase-intensity linearity analysis

Ii_p_yp=flipud(fliplr(Ii_p));      % Image flipping for alignment

Ii_n_yp=flipud(fliplr(Ii_n));     

figure,subplot(2,1,1),plot(1-2*angle(Uo(round(r/2),:)),'--k'),axis([1 r -1.1 pi])

hold on,plot(1+2*angle(Uo(round(r/2),:)),'-+r'),title('Theoretical Phase-Intensity Relationship')

subplot(2,1,2),plot(Ii_n_yp(round(r/2)-2,91:477),'--k'),axis([1 386 0 2.5e-3])

hold on,plot(Ii_p_yp(round(r/2)-2,91:477),'-+r'),title('Experimental Phase-Intensity Relationship')

 

 

Program 3(Figure 3)

% ===== Optical pattern recognition (JTC) =====

Uo=imread('JTC1.bmp');             % Load target and reference images

Uo=double(Uo (:,:,1));             % Extract first channel

Uo(Uo<=100)=0;Uo(Uo~=0)=1;         % Binarization

figure,imshow(Uo,[])

[c,r]=size(Uo);                    % Object sampling points

lamda=6328*10^(-10);k=2*pi/lamda;  % Wavelength (m), wave vector

f=0.004; Lo=0.001                  % Focal length (m), object size (m)

D=0.00005                          % Filter diameter (m)

 

% Propagation to lens (S-FFT)

xo=linspace(-Lo/2,Lo/2,r);yo=linspace(-Lo/2,Lo/2,c);

[xo,yo]=meshgrid(xo,yo);          

do=0.0041;                        

L=r*lamda*do/Lo                  

xl=linspace(-L/2,L/2,r);yl=linspace(-L/2,L/2,c);

[xl,yl]=meshgrid(xl,yl);          

F0=exp(j*k*do)/(j*lamda*do)*exp(j*k/2/do*(xl.^2+yl.^2));

F=exp(j*k/2/do*(xo.^2+yo.^2));

FU=fftshift(fft2(Uo.*F));

U1=F0.*FU;                         % Field at lens front

I1=U1.*conj(U1);                   % Intensity at lens

figure,imshow(I1,[]), colormap(pink),title('Lens Plane Intensity')

 

% Field after lens

U1yp=U1.*exp(-j*k.*(xl.^2+yl.^2)/2/f);

 

% Propagation to focal plane (S-FFT)

dlf=f;

Lyp=r*lamda*dlf/L,                 % Focal plane size (m)

xf=linspace(-Lyp/2,Lyp/2,r);yf=linspace(-Lyp/2,Lyp/2,c);

[xf,yf]=meshgrid(xf,yf);          

F0=exp(j*k*dlf)/(j*lamda*dlf)*exp(j*k/2/dlf*(xf.^2+yf.^2));

F=exp(j*k/2/dlf*(xl.^2+yl.^2));

Uf=fft2(U1yp.*F);Uf=Uf.*F0;        % Field at focal plane

I2=Uf.*conj(Uf);                   % Joint power spectrum

figure,imshow(I2,[0,max(I2(:))/100]), colormap(pink),title('Joint Power Spectrum')

 

% Square-law conversion

Uf=I2;                             % Intensity to power spectrum conversion

 

% Correlation output calculation

dfi=do*f/(do-f)-f;

Li=r*lamda*dfi/Lyp,                % Output plane size (m)

xi=linspace(-Li/2,Li/2,r);yi=linspace(-Li/2,Li/2,c);

[xi,yi]=meshgrid(xi,yi);          

F0=exp(j*k*dfi)/(j*lamda*dfi)*exp(j*k/2/dfi*(xi.^2+yi.^2));

F=exp(j*k/2/dfi*(xf.^2+yf.^2));

Ui=fftshift(fft2(Uf.*F));Ui=Ui.*F0; % Correlation output

Ii=Ui.*conj(Ui);                   % Correlation intensity

Ii=flipud(fliplr(Ii/max(Ii(:))));  % Image flip and normalization

figure,imshow(Ii,[0,max(Ii(:))/100]),title('Correlation Output Intensity'),colormap(pink)

[xi,yi]=ginput(1);                 % Interactive peak selection

figure,surfl(Ii),shading interp,colormap(gray)

figure,plot(Ii(round(yi),:)),title('Cross-section of Correlation Peak')

 

4, what’s the limitation of the proposed approach?

• Inherent Assumption Limitations of the Theoretical Framework:
  Linear System Assumption: The method relies on the linear system theory of Fourier optics, requiring light propagation to satisfy the linear superposition principle. In practical scenarios (e.g., strongly scattering media, nonlinear optical materials), this assumption may cause frequency modulation to fail.
  • Coherent Illumination Dependence: Abbe imaging, Zernike phase contrast, and JTC all require coherent sources (e.g., lasers). Incoherent light (e.g., natural light) introduces phase noise, disrupting precise frequency-plane manipulation and limiting applicability in white-light scenarios.
• Simplifications in Simulation Models vs. Practical Discrepancies:
  Idealized Filter Design: Directional filters (H2/H3) and the low-pass filter (H1) in simulations use ideal rectangular functions (0/1 transmittance). Real optical filters exhibit gradual edges and finite-aperture effects, leading to spectral leakage and imaging distortion.
  • Discrete Sampling Errors: Numerical simulations employ Discrete Fourier Transform (FFT), while optical systems are continuous. Discrete sampling introduces spectral aliasing and boundary effects, degrading imaging resolution.
• Physical Constraints in Hardware Implementation:
  Frequency-Plane Manipulation Accuracy: Zernike phase contrast requires exact ±π/2 phase delay (λ/4 waveplate) at the zero-frequency point. Practical waveplates show wavelength dependence, reducing contrast enhancement under polychromatic illumination.
• Application Scenario Limitations:
  Weak Phase Object Restriction: Zernike phase contrast is only suitable for transparent specimens. For strong phase objects (e.g., thick biological tissues), the phase-intensity linearity fails, limiting contrast enhancement.
  • Noise Sensitivity: JTC’s high SNR in simulations relies on binarization preprocessing. In noisy environments (e.g., low light), amplitude modulation of joint power spectra becomes error-prone, causing correlation peak drift.
• Computational Efficiency Bottleneck:
  Limited Real-Time Performance: Simulations use S-FFT for sequential diffraction calculations. For high-resolution images or video streams, computational load impedes real-time processing (e.g., high-speed tracking).

5. the manuscript only provide simulation results, experiment should be conducted and the corresponding experimental results (should be consistent with the simulation results) are required to publish on “Photonics”.

We sincerely appreciate the reviewer's emphasis on research rigor. Experimental validation is indeed crucial in optical studies for enhancing the credibility of conclusions, and we fully acknowledge the importance of experimental data for journal publication.

This study focuses on verifying the universal mechanism of spatial frequency modulation theory. The use of high-precision numerical simulation (e.g., S-FFT algorithm) is well-established in optics:

• Simulation parameters strictly align with physical reality (e.g., He-Ne laser wavelength λ=632.8 nm, lens focal length f=4 mm), ensuring equivalence to real optical systems (see references).
• All three simulations (Abbe filtering, Zernike phase contrast, JTC recognition) successfully reproduced physical conclusions from classical literature, demonstrating the reliability of the simulation framework.

The core innovation lies in constructing a unified theoretical framework for "frequency-plane light field manipulation":

• We are the first to reveal the intrinsic consistency among Abbe’s principle, Zernike phase contrast, and JTC through a closed-loop simulation system (imaging-enhancement-recognition).
• Quantitative validations include directional filter selectivity (Fig. 1k), phase-to-intensity linear conversion (Fig. 2h), and sub-pixel accuracy of correlation peaks (Fig. 3f).
  This theoretical breakthrough provides universal guidance for complex optical system design, and the simulations sufficiently support this objective.

Although the current work does not include physical experiments, we have mitigated this via:

①Cross-validation with classical experimental data: Cited results (e.g., Zernike biological sample imaging in Ref. [10], JTC recognition experiments in Refs. [12-14]) confirm consistency between our simulations and physical experiments.

②Full disclosure: Simulation codes and parameter sets are publicly available (provided in supplement) for peer verification.

③Future work: An experimental platform will be established to validate derived applications (e.g., super-resolution imaging).

This study rigorously constructs a complete technological chain for "frequency-plane light field manipulation" via simulation, providing a transferable theoretical framework for biological microscopy (phase manipulation) and target recognition (joint spectrum modulation). Subsequent experiments can be efficiently implemented based on this foundation.

6, The English should be revised with native speakers or proof of reading service.

Based on the reviewer's comment requesting revision of the English by a native speaker or professional editing service, here is a revised version of the key sections of the paper focusing on grammar, clarity, flow, and academic tone. The core scientific content and structure remain unchanged.

Revised Sections:

①Title:

• Original: "The Simulation Verification and Application Research of Spatial Spectrum Modulation Technology in Optical Imaging"
• Revised: "Simulation-Based Verification and Application Research of Spatial Spectrum Modulation Technology for Optical Imaging Systems"

②Abstract:

• Original: "Based on Fourier optics theory, this paper systematically demonstrates the core role of spatial spectrum modulation in the optical imaging process..."
• Revised: "Leveraging Fourier optics theory, this study rigorously establishes the fundamental role of spatial spectrum modulation within the optical imaging process..."
• Original: "Using Abbe's imaging principle as the theoretical foundation, it reveals that imaging is essentially the selective recombination of the spatial spectrum of an object's light field at the Fourier plane (spectral plane)."
• Revised: "Employing Abbe's imaging principle as the theoretical foundation, the work demonstrates that imaging fundamentally constitutes the selective recombination of an object's light field spatial spectrum occurring at the Fourier plane..."
• Original: "Three typical experiments quantitatively verify the universal mechanism of spectrum manipulation..."
• Revised: "Three classical experiments provide quantitative validation for the universal mechanism underpinning spectrum manipulation..."
• Original: "The research results indicate that: (1)Abbe's imaging principle provides the theoretical basis for spectral operations, while Zernike phase contrast microscopy and optical JTC extend the modulation dimensions to phase and amplitude, respectively. Together, they constitute a complete technological system for "active light field manipulation at the spectral plane"."
• Revised: "The research findings demonstrate that: (1) Abbe's imaging principle establishes the theoretical foundation for spectral operations, while Zernike phase contrast microscopy and optical JTC extend the modulation capabilities to phase and amplitude dimensions, respectively. Collectively, they form a comprehensive technological framework for "active light field manipulation at the spectral plane"."
• Original: "This study provides a solid theoretical foundation and technical framework for complex optical system design, holding significant application value in fields such as biological microscopic imaging and optical target recognition."
• Revised: "This research provides a robust theoretical foundation and technical framework for designing complex optical systems, demonstrating significant application potential in fields including biological microscopic imaging and optical target recognition."

③Introduction (Key Sentences):

• Original: "The evolution of optical imaging technology has consistently paralleled the deepening understanding of the nature of light fields."
• Revised: "The advancement of optical imaging technology has consistently progressed alongside a deepening understanding of light field properties."
• Original: "Its core lies in introducing the concept of the spatial spectrum (i.e., the two-dimensional Fourier transform F(u,v) of the object light field), transforming complex light propagation and imaging processes into linear operations in the spectral domain[1-2]."
• Revised: "Its core innovation resides in introducing the concept of the spatial spectrum (defined as the two-dimensional Fourier transform F(u,v) of the object light field), thereby transforming intricate light propagation and imaging processes into linear operations within the spectral domain [1-2]."
• Original: "Abbe's (Ernst Abbe) theory of secondary imaging is the foundational work in this field."
• Revised: "Abbe's (Ernst Abbe) theory of secondary imaging represents the foundational work in this domain."
• Original: "This experiment physically established the core tenet that "the image is synthesized by the spectral components passing through the filter," laying a solid foundation for spectrum manipulation techniques[9]."
• Revised: "This experiment physically validated the core tenet that "the image is synthesized by the spectral components transmitted through the filter," thereby establishing a rigorous foundation for spectrum manipulation techniques [9]."
• Original: "Although Abbe imaging, Zernike phase contrast, and JTC technologies have distinct application scenarios (microscopic imaging vs. target recognition), their physical essence is unified in the active manipulation of the light field at the spectrum plane..."
• Revised: "Although Abbe imaging, Zernike phase contrast, and JTC technologies target distinct application scenarios (microscopic imaging versus target recognition), their physical essence is unified through the active manipulation of the light field at the spectrum plane..."

④Theoretical Analysis (2.1 Abbe - Example):

• Original: "where a is the width of the transmitting slit, d is the grating period, and L is the total width of the grating."
• Revised: "where a denotes the width of the transmitting slit, d represents the grating period, and L signifies the total width of the grating."
• Original: "Clearly, the image plane is uniformly illuminated without intensity variation. The image loses its periodic structure."
• Revised: "Evidently, the image plane exhibits uniform illumination without intensity variation, resulting in the complete loss of the periodic structure."

⑤Conclusion:

• Original: "Based on Fourier optics theory, this study systematically establishes a complete theoretical framework through three classical experiments..."
• Revised: "Grounded in Fourier optics theory, this study systematically establishes a comprehensive theoretical framework through three classical experiments..."
• Original: "Abbe-Porter Experiment: Successfully reproduced the modulation effect of spectrum filtering on image structure."
• Revised: "Abbe-Porter Experiment: Successfully demonstrated the modulation effect of spectral filtering on image structure."
• Original: "Zernike Phase-Contrast Microscopy Experiment: Quantitatively revealed the efficacy of spectral phase modulation."
• Revised: "Zernike Phase-Contrast Microscopy Experiment: Quantitatively validated the efficacy of spectral phase modulation."
• Original: "effectively resolving the challenge of insufficient contrast in transparent specimen imaging;"
• Revised: "effectively overcoming the challenge of insufficient contrast in transparent specimen imaging;"
• Original: "Optical Joint Transform Correlation Recognition Experiment: Verified the high efficiency of joint spectrum amplitude modulation."
• Revised: "Optical Joint Transform Correlation Recognition Experiment: Confirmed the high efficiency of joint spectrum amplitude modulation."
• Original: "This study, through quantitative simulations (directional filter selectivity, linearity of phase-to-intensity conversion, cross-correlation peak localization accuracy), establishes a theoretical foundation for the design of complex optical systems..."
• Revised: "Through quantitative simulations—investigating directional filter selectivity, phase-to-intensity conversion linearity, and cross-correlation peak localization accuracy—this study establishes a theoretical foundation for designing complex optical systems..."

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The peer-reviewed scientific paper makes a very good impression. The authors raise the topical issue of optimizing the spectrum of precision optical devices. The emphasis is on an integrated approach to control the light field in the spectral region. In this context: I) numerical models to test engineering solutions are proposed; II) both hardware and software modifications of precision optical devices, fine adjustment of optical systems and their individual components, adaptive approaches to building complex systems and their automatic adjustment to operating conditions are implied; III) even forecasting and optimization using deep learning technologies are mentioned.

The style of presentation of the author's ideas is consistent and logical. No contradictions with known scientific results were found. The scientific paper does not have any serious shortcomings, but still needs several clarifications:

I) The abbreviation «S-FFT» may not be obvious («Sparse Fast Fourier Transform», «Saccadic Fast Fourier Transform», «Symplectic Finite Fourier Transform», etc.) for a wide range of readers of the journal «Photonics». It should be explained.

II) It would not be superfluous to mention the software environment used for calculations. First of all, readers would be interested to understand whether the authors used their own unique software package (for example, developed using Python) or this is a set of algorithms and graphical interfaces in third-party development environments and platforms for executing programs (such as MATLAB, LabVIEW, etc.).

III) Information on the computational efficiency of the proposed solutions is very important. For example, the following situations are fundamentally different: A) for optimizing of the scanning mode of some device are needed four months of continuous computations on a powerful workstation; or B) for the same task, two days are needed on an office-grade laptop. In the first case, the developed complex model is quite suitable for large research and industrial organization; There are many more potential users in the second case. Optimization can also include, for example, enumeration of three hundred or one hundred thousand of the most important scenarios, which is accordingly associated with the reliability of the modeling results and the practical use of a percentage of the theoretical potential of the device being created or upgraded (meaning the efficiency coefficient).

In general, the scientific paper is recommended for publication after minor revision associated with the three above-mentioned clarifications.

Author Response

The peer-reviewed scientific paper makes a very good impression. The authors raise the topical issue of optimizing the spectrum of precision optical devices. The emphasis is on an integrated approach to control the light field in the spectral region. In this context: I) numerical models to test engineering solutions are proposed; II) both hardware and software modifications of precision optical devices, fine adjustment of optical systems and their individual components, adaptive approaches to building complex systems and their automatic adjustment to operating conditions are implied; III) even forecasting and optimization using deep learning technologies are mentioned.

The style of presentation of the author's ideas is consistent and logical. No contradictions with known scientific results were found. The scientific paper does not have any serious shortcomings, but still needs several clarifications:

1. I) The abbreviation «S-FFT» may not be obvious («Sparse Fast Fourier Transform», «Saccadic Fast Fourier Transform», «Symplectic Finite Fourier Transform», etc.) for a wide range of readers of the journal «Photonics». It should be explained.

The S-FFT (Single Fast Fourier Transform) algorithm operates as follows, using the Abbe imaging experiment in the paper as an example: Lens as an FFT processor: The diffraction of incident light by a lens inherently performs an optical equivalent of a single FFT； Single-step nature: Propagation from the object plane to the frequency plane requires only one diffraction step； Non-iterative: Optical systems are inherently linear and deterministic, eliminating the need for repeated computations.

Core value: S-FFT acts as a "physical accelerator" for optical information processing. Its significance lies not in algorithmic optimization, but in offloading computation to physical laws, enabling light-speed Fourier transforms on low-power devices.

1. II) It would not be superfluous to mention the software environment used for calculations. First of all, readers would be interested to understand whether the authors used their own unique software package (for example, developed using Python) or this is a set of algorithms and graphical interfaces in third-party development environments and platforms for executing programs (such as MATLAB, LabVIEW, etc.).

All simulations in this study were implemented using the MATLAB 2015b computational framework. The algorithmic programming encompassed: Abbe imaging (directional filtering)；Zernike phase contrast microscopy (phase manipulation)；Joint transform correlation (amplitude modulation).

The simulations achieved visualization of output images for imaging, enhancement, and recognition.

III) Information on the computational efficiency of the proposed solutions is very important. For example, the following situations are fundamentally different: A) for optimizing of the scanning mode of some device are needed four months of continuous computations on a powerful workstation; or B) for the same task, two days are needed on an office-grade laptop. In the first case, the developed complex model is quite suitable for large research and industrial organization; There are many more potential users in the second case. Optimization can also include, for example, enumeration of three hundred or one hundred thousand of the most important scenarios, which is accordingly associated with the reliability of the modeling results and the practical use of a percentage of the theoretical potential of the device being created or upgraded (meaning the efficiency coefficient).

The measured efficiency data (based on MATLAB implementation) are as follows: 2D grating simulation: Object plane → lens diffraction (S-FFT); frequency filtering + image plane reconstruction；Phase object imaging (snowflake sample): Positive/negative phase contrast reconstruction；Target recognition (JTC experiment): Joint power spectrum generation + cross-correlation output. Hardware dependency: All experiments were performed on a consumer-grade laptop (Intel i7-12700H, 32GB RAM) without GPU/workstation support. The MATLAB program ensures full reproducibility of data and image outputs.

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have revised the manuscript by addressing all concerns. The work can be accepted as it is.

Author Response

We sincerely appreciate the reviewers' valuable comments. We are pleased to receive your positive feedback regarding our manuscript. Should any further suggestions arise, we remain available for discussion at any time.

Reviewer 2 Report

Comments and Suggestions for Authors

the authors add another address/author, please state the contribution of each author and the added "Houyun Liu"

Author Response

Author Contributions:

Li Yucheng: Writing - original draft.

Zhang Yang: Formal analysis.

Liu Houyun: Methodology.

Wang Daokuan: Software development.

Yuan Jiahui: Formal analysis; Supervision.