Suppressing the Zero-Frequency Components in Single Quantitative Phase Imaging by Filtering the Low-Frequency Intrinsic Mode Function Components
Round 1
Reviewer 1 Report (Previous Reviewer 1)
The authors have revised the manuscript according to most of the comments. However, the method proposed in this paper still lacks sufficient innovation and unique advantages. It has been noted that fringe demodulation using EMD and HT has been proposed for many years, and there is a lot of related work from the group of Trusiak et al. In contrast, the authors seem to present only the basic principles of the method without any improvement. Therefore, the authors are required to highlight the differences and advantages of their method proposed in the paper with respect to previous reconstruction using BMD and HT methods. Additionally, it is advisable to include corresponding text descriptions for the figures in the manuscript to improve presentation of the results.
The English grammar and vocabulary of this article are basically fine.
Author Response
Response to Reviewer 1 Comments
The authors have revised the manuscript according to most of the comments. However, the method proposed in this paper still lacks sufficient innovation and unique advantages. It has been noted that fringe demodulation using EMD and HT has been proposed for many years, and there is a lot of related work from the group of Trusiak et al. In contrast, the authors seem to present only the basic principles of the method without any improvement. Therefore, the authors are required to highlight the differences and advantages of their method proposed in the paper with respect to previous reconstruction using BMD and HT methods. Additionally, it is advisable to include corresponding text descriptions for the figures in the manuscript to improve presentation of the results.
Response : Great thanks for the suggestions from reviewer 1. We have added many descriptions of the proposed methods in this paper and made the improvements more specific. In our paper, we decompose the hologram into a series of intrinsic mode function (IMF) components from high to low frequencies, the low-frequency IMF components are filtered by Gaussian high-pass filter to preserve the high-frequency information. The filtered low-frequency IMF components are combined with the high-frequency IMF components to generate a reconstructed hologram. Then the reconstructed hologram is processed by the Hilbert transform to remove the zero frequency component (ZFC) and conjugate image, leaving only the original image.
Compared with the method in ref[29,30], the proposed method avoids from discarding the low-frequency IMF components directly, thus preserves the high-frequency phase information. In Figs. 5 and 7, we can see the reconstructed phase distribution obtained by the proposed method is fuller and smoother, with fewer missing parts. In contrast, the reconstruction results of the other three ZFC suppression methods show that the reconstruction results of the traditional Fourier filtering method, the Harr wavelet transform, and the Laplace algorithm all have significant detail missing. In Fig. 5(b) and Fig. 7(b,f), the edges of the small raised squares are cluttered and some of the small squares are clearly missing in the lower left corner. There is also some loss in the central part of Fig. 5(a) and Fig. 7(a,e). Quantitative analysis such as peak signal-to-noise ratio(PSNR), structural similarity (SSIM) and cross-sectional curves are carried out to evaluate the performance of reconstructed phases of different methods. The superiority of the method proposed in this paper is illustrated in Table 1-5. In summary, the method proposed in this paper preserves high-precision phase information and remove the ZFC and conjugate image.
The detailed description on the experimental results are also added in the revised paper to make the conclusion more clear.
Reviewer 2 Report (Previous Reviewer 3)
Authors improved the mansucript, so now I can suggest to accept it for publication.
Author Response
Response to Reviewer 2 Comments
Authors improved the mansucript, so now I can suggest to accept it for publication.
Response: Thank you for your careful review of my manuscript and your positive comments. Your suggestions and comments have guided us effectively in making improvements and making the manuscript more acceptable. We sincerely appreciate your help and support.
Reviewer 3 Report (New Reviewer)
Filtering method for suppression zero-frequency component of digital hologram by combination of algorithm for extracting low-frequency intensity oscillations in a digital hologram, applying a Gaussian filter and a Hilbert transform is proposed.
A more detailed and structured description of the method is required. In particular, there is no explanation of how the Hilbert transform makes it possible to suppress the virtual image.
The proposed method, which at one stage suppresses the zero frequency component and at the second stage suppresses the virtual image, is compared with algorithms that only suppress the zero frequency component. In order to the comparison to be correct, after applying the traditional Fourier filtering, Haar wavelet transform and Laplace operator methods, the Hilbert transform should be applied similarly to the proposed method to get rid of the virtual (conjugate) image.
When comparing the results of the method with other methods, it naturally turns out that the results are very close to traditional Fourier filtering. What the reason for using proposed method?
The Abstract states that the zero frequency component affects the resolution of the reconstructed image, but neither the results nor conclusion quantify the improvement in image resolution after applying the proposed method.
It is advisable for authors to read the following articles:
E. Cuche, P. Marquet, Ch. Depeursinge “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography” Applied Optics. 2000. Vol. 39, â„– 23. P. 4070–4075.
S. Pasko, R. Jozwicki “Improvement methods of reconstruction process in digital holography” Opto-Electronics Review. 2003. Vol. 11, â„– 3. P. 203–209.
G.-L. Chen, C.-Y. Lin, M.-K. Kuo, C.-C. Chang “Numerical suppression of zero-order image in digital holography” Optics Express. 2007. Vol. 15, â„– 14. P. 8851–8856.
H. Halaq, Y. Takakura, D. Vukicevic “Zero order elimination for digital holograms: study of setup dependent methods” 2019 International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS). Taza, 2019.
Check the use of notations in the text. So, for example, notations u(x, y) и v(x, y) coincides with the notation of the frequencies u и v. Starting from line 172, the designations t, t1 и t2, appear, not related to the previous mathematical calculations. On lines 53-54 in the sentence «High-quality image recovery is possible even when the DC and cross terms in the hologram overlap in the Fourier domain» DC is not defined.
Authors are encouraged to check the English text with a qualified interpreter of native speaker.
At the same time, it is also necessary to formulate sentences more correctly so that there are no sentences like: «and preserve the high-frequency information in the low-frequency IMF components» (lines 75-76), «According to Eq. (1), digital hologram is typically nonlinear function» (line 100); «Firstly, we find out the local maximum value and the local minimum value in the image (???). Then the local maximum and local minimum surfaces are constructed by interpolation, respectively …» (lines 110-112). Line 214 says «The original phase objects are shown in Fig. 3(a), 214 Fig. 3(b) and Fig. 3(c),» although from the figure it is more likely to say that some of them are an amplitude objects.
Avoid excessive use of abbreviations, especially in the abctract and in the conclusion. These sections should give an idea of the material of the entire article withaout reading it. I do not think it is possible with this conclusion (lines 387-393):
In this paper, we propose an HT-based Gaussian high-pass filtering method to suppress the ZFC of QPI with only one shot. Through the Mach-Zehnder recording optical system, the captured hologram firstly is decomposed by EMD to a series of IMF components from high to low frequency components. Since the low-frequency components represent the ZFC of the hologram, so we process the low-frequency IMF components taining ZFC with Gaussian high-pass filtering to obtain the ZFC-suppressed data，and then reconstruct the original signal together with the high-frequency IMF components 393 that do not contain ZFC.
Authors are encouraged to check the English text with a qualified interpreter of native speaker.
Author Response
Response to Reviewer 3 Comments
Filtering method for suppression zero-frequency component of digital hologram by combination of algorithm for extracting low-frequency intensity oscillations in a digital hologram, applying a Gaussian filter and a Hilbert transform is proposed.
Point 1: A more detailed and structured description of the method is required. In particular, there is no explanation of how the Hilbert transform makes it possible to suppress the virtual image.
Response: Great thanks for the suggestions from reviewer 3. We have provided a more detailed and structured description of the method proposed in this paper and explained how the Hilbert transform suppresses the virtual image. To perform the Hilbert transform on the hologram after ZFC suppression, the hologram is first Fourier transformed to extract the frequency domain information, and then filtered by applying a function orthogonal to the original signal spectrum and Fourier inverse transformed to obtain the filtered hologram. By this process, the frequency components of the virtual image are suppressed, while the frequency components of the original image are preserved.
Point 2: The proposed method, which at one stage suppresses the zero frequency component and at the second stage suppresses the virtual image, is compared with algorithms that only suppress the zero frequency component. In order to the comparison to be correct, after applying the traditional Fourier filtering, Haar wavelet transform and Laplace operator methods, the Hilbert transform should be applied similarly to the proposed method to get rid of the virtual (conjugate) image
Response 2: Thank you for the suggestion. We have revised the experimental section by using the conventional Fourier filter, Haar wavelet transform, and Laplace operator to suppress the zero frequency component in the first stage and the Hilbert transform to remove the virtual images (conjugate image) in the second stage before comparing them with the method proposed in this paper. The results are shown in Figure 6 in the revised paper.
Point 3: When comparing the results of the method with other methods, it naturally turns out that the results are very close to traditional Fourier filtering. What the reason for using proposed method?
Response 3: Since the frequency components of original image, zero-level image and conjugate images of hologram may overlap in frequency domain, the traditional Fourier filtering method is difficult to achieve satisfactory for these cases. For the case that the original image, the zero-level image and the conjugate images overlap in frequency domain, the proposed method in this paper can suppress the zero-frequency component without losing the high-frequency information of original image. The calculated results of PSNR and SSIM also show that the phase reconstruction accuracy of the proposed method in this paper is higher than other methods.
Point 4: The Abstract states that the zero frequency component affects the resolution of the reconstructed image, but neither the results nor conclusion quantify the improvement in image resolution after applying the proposed method.
Response 4: Existing methods of suppressing zero frequency component always lose the high-frequency components, so we state that the resolution of reconstructed hologram will be affected in the previous manuscript. To avoid misunderstanding, in the revised paper we delete the statement and replace it with the effect on the reconstructed phase accuracy.
Point 5: It is advisable for authors to read the following articles:
- Cuche, P. Marquet, Ch. Depeursinge “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography” Applied Optics. 2000. Vol. 39, â„– 23. P. 4070–4075.
- Pasko, R. Jozwicki “Improvement methods of reconstruction process in digital holography” Opto-Electronics Review. 2003. Vol. 11, â„– 3. P. 203–209.
G.-L. Chen, C.-Y. Lin, M.-K. Kuo, C.-C. Chang “Numerical suppression of zero-order image in digital holography” Optics Express. 2007. Vol. 15, â„– 14. P. 8851–8856.
- Halaq, Y. Takakura, D. Vukicevic “Zero order elimination for digital holograms: study of setup dependent methods” 2019 International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS). Taza, 2019.
Response 5: Thank you for the suggestion. We have studied these articles to improve the work and cited them in the revised paper.
Point 6: Check the use of notations in the text. So, for example, notations u(x, y) и v(x, y) coincides with the notation of the frequencies u и v. Starting from line 172, the designations t, t1 и t2, appear, not related to the previous mathematical calculations. On lines 53-54 in the sentence «High-quality image recovery is possible even when the DC and cross terms in the hologram overlap in the Fourier domain» DC is not defined.
Response 6: Thank you for the suggestion. We have changed the expressions for the maximum and minimum surfaces from u(x,y) and v(x,y) to a(x,y) and b(x,y) , so that they can be distinguished from the frequency symbols u and v. The meaning of t, t1 and t2 have been explained in the text. Where t represents the time coordinate of a one-dimensional signal, which varies over the range of the real signal, while t1 and t2 represent the time variable of a two-dimensional signal, which is the position or coordinate of the signal in a different dimension. A complete definition of the direct-current (DC) has been given.
Point 7: Authors are encouraged to check the English text with a qualified interpreter of native speaker.
Response 7: Thank you for the suggestion. We have checked the paper thoroughly and corrected inappropriate phrases or grammatical errors.
Point 8: At the same time, it is also necessary to formulate sentences more correctly so that there are no sentences like: «and preserve the high-frequency information in the low-frequency IMF components» (lines 75-76), «According to Eq. (1), digital hologram is typically nonlinear function» (line 100); «Firstly, we find out the local maximum value and the local minimum value in the image (???). Then the local maximum and local minimum surfaces are constructed by interpolation, respectively …» (lines 110-112). Line 214 says «The original phase objects are shown in Fig. 3(a), 214 Fig. 3(b) and Fig. 3(c),» although from the figure it is more likely to say that some of them are an amplitude objects.
Response 8: Thank you for the suggestion. The inappropriate sentences mentioned above have been revised.
Point 9: Avoid excessive use of abbreviations, especially in the abctract and in the conclusion. These sections should give an idea of the material of the entire article withaout reading it. I do not think it is possible with this conclusion (lines 387-393):
In this paper, we propose an HT-based Gaussian high-pass filtering method to suppress the ZFC of QPI with only one shot. Through the Mach-Zehnder recording optical system, the captured hologram firstly is decomposed by EMD to a series of IMF components from high to low frequency components. Since the low-frequency components represent the ZFC of the hologram, so we process the low-frequency IMF components taining ZFC with Gaussian high-pass filtering to obtain the ZFC-suppressed data，and then reconstruct the original signal together with the high-frequency IMF components 393 that do not contain ZFC.
Response 9: Thank you for the suggestion. We have modified the conclusion to make them easy to understand.
Round 2
Reviewer 1 Report (Previous Reviewer 1)
This manuscript has been improved sufficiently to warrant publication in Photonics.
Reviewer 3 Report (New Reviewer)
The manuscript has been improved according to reviewer comments
The manuscript has been improved according to reviewer comments
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
In this manuscript, the author proposed a Hilbert-Huang transform based method that only needs one image and avoids manually adjusting the layer of decomposition. The hologram is decomposed into a series of IMF components from high to low by EMD, and HT is performed on the new hologram which is composed of high-frequency components to recover the complex amplitude. Overall, the principle of the proposed method is quite simple. However, the innovativeness and the significance of this paper are insufficient for its publication in Photonics. Firstly, fringe demodulation using EMD and HT has been proposed for many years, and there are a lot of related work from the group of Trusiak et al. In contrast, the authors only present the basic principle of the method without any improvement. Secondly, the authors note that existing methods for suppressing ZFC should record multiple images with additional devices. However, various zero-order suppression methods have been proposed in recent years [1-4], and all of them only require one hologram. At last, the figures in the manuscript are of very low quality and the experimental results are not clearly presented. The method proposed in this paper lacks sufficient innovation and unique advantages. Therefore, I do not recommend this manuscript to be published in Photonics.
[1] Pavillon N, Arfire C, Bergoënd I, et al. Iterative method for zero-order suppression in off-axis digital holography[J]. Optics Express, 2010, 18(15): 15318-15331.
[2] Khare K, Ali P T S, Joseph J. Single shot high resolution digital holography[J]. Optics express, 2013, 21(3): 2581-2591.
[3] Baek Y S, Lee K R, Shin S, et al. Kramers–Kronig holographic imaging for high-space-bandwidth product[J]. Optica, 2019, 6(1): 45-51.
[4] Shen Q, Sun J, Fan Y, et al. High-throughput artifact-free slightly off-axis holographic imaging based on Fourier ptychographic reconstruction[J]. Front. Photonics, 2022, 3: 936561.
Reviewer 2 Report
In the manuscript, Meng et al. proposed the zero-frequency component suppression with Hilbert-Huang transform, and demonstrated its application in single-shot quantitative phase imaging. Personally, I don’t think the manuscript is suitable for publication in Photonics. The details are shown below.
1. The quality of the figures is very poor. It is difficult to observe the details of the figures. The color bar is missed. The labels are unclear.
2. The results in the tables are confusing. The author used standard deviation to evaluate the imaging quality, with a smaller value corresponding to a higher accuracy. The original phase map should be the ground truth. Then the standard deviation of the proposed method is smaller than the ground truth? It is difficult to understand such a conclusion.
3. From Fig.6(a-d), the off-axial component is clearly separated from the central component. Therefore, the off-axial component can be easily chosen and used to solve the phase of object beam. To show the superiority the proposed method, a holography with the off-axial component and central component overlap is more suitable.
4. Also, the writing should be improved.
Reviewer 3 Report
In this work, the athors propose a method to suppress the Zero Frequency Component (ZFC) of the Quantitative Phase Imaging (QPI) by using the decomposition of the a single captured hologram in a Intrinsic Mode Function (IMF) components from high to low frequencies. Hilbert Tranform (HT) is finally used to filter out the conjugate componet in the reconstructed hologram and potentially improve reconstruction accuracy.
The manuscript describes the principle of the method and an experimental characterization based on the analysis of phase objects with QPI, implemented via a Mach-Zehnder interferometer.
Although themanusctipt is potentially well organized, low-resolution figures and highly repetitive text and labels in the experimental description and figure captions make the manuscript very difficult to read. In my opinion, the presentation must be improved before considering the manuscript acceptable for publication.
Here below some additional comment.
1) I would suggest to include additional comments about each step of EMD and its effect on a hologram. Adding a schematic figure to visually explain the effect of including more Ci terms in the decomposition would be benficial.
2) There are no ground-truth experimental characterization of the objects measured in the manuscript, and the very bad quality of the figures (figure axis missing scalebars, etc.) does not allow any reasonable comparison.
3) How the effect of removing the ZFC should be visible in from the presented data? The authors should additionally comment across the data discussion in the paper.
4) Why the standard deviation should be considered as appropriate chacterization of the retrieved phase map accuracy with the different methods? Without knowing the details of the sample, a reduced standard deviation does not directly imply higher accuracy.
Reviewer 4 Report
In this manuscript, the authors propose a method to suppress the zero-frequency component in off-axis digital holography. This method uses Empirical Mode Decomposition to decompose the hologram into a series of Intrinsic Mode Function components from high to low frequencies. Then they reconstruct the hologram only with high-frequency components and perform Hilbert Transform on the hologram to filter out the conjugate image.
Actually, suppression of the DC term in digital holography is an old topic and many strategies have been proposed. From my point of view, suppression of DC term is required only in on-axis digital holography because the DC term and conjugate image can be easily and effectively eliminated by spectral filtering on the spectrum image of the off-axis hologram. Thus, the impact of this manuscript is relatively weak. In addition, (1) it’s not convincing to compare the phase map accuracy by calculating the standard deviation of the phase map (Eq. 12). (2) The DC term is not completely removed and some high frequency corresponding to the real image is destroyed, as shown in Figs. 4 and 6 in the manuscript. (3) Many expressions are not professional or rigorous, such as 1) the first sentence in Introduction part. The truth is that quantitative phase imaging can be realized not only by interference method but also by non-interference method. 2) Line 47: …the result of ZFC suppression is not “good” because the frequency…, what’s the meaning of “good”?
In conclusion, the novelty, impact, and technical details of the present manuscript are all in low level, and I cannot recommend its publication on Photonics.
