Suppression for Phase Error of Fringe Projection Profilometry Using Outlier-Detection Model: Development of an Easy and Accurate Method for Measurement
Round 1
Reviewer 1 Report
In this paper, an easy-to-implement calibration method based on the (RANSAC) algorithm is proposed to eliminate the phase error data in the fringe projection system, which improves the accuracy of the measurement to a certain extent. The following modifications are recommended:
1. The second part of the article does not explain the principle of RANSAC and how it is applied to the projection fringes in detail, please add a description of this.
2. In the second part of the text, select a set of vertical lines from 150 to 1770 pixels at 60 pixel intervals, please explain the reason for the 60 pixel interval. It is also recommended to illustrate through pictures.
3. In the third part/fourth part of the paper, the relevant process details of the experiment are added to highlight the importance of the proposed method.
4. Please ask whether other factors such as the gamma distortion effect are taken into account when analyzing the error, and explain the basis for compensation by this method.
5. Whether this method is also applicable to other unwrapping methods, or is it only for three-frequency heterodyne unwrapping method.
6. In the fourth part, it is recommended to use LSM, RANSAC compensation and uncompensated experimental results (such as phase diagrams, etc.) for comparison.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
This paper proposed a monocular phase-shifting fringe projection profilometry based on the geometric constraint equations for three-dimensional measurement. To reduce the measurement uncertainties, a calibration method based on the Random Sample Consensus algorithm is proposed. The results have shown a good improvements with the traditional least squared method. However, for reader to understand the fundamental principle of the method, the following technical sections should be given in this paper:
1. A schematic diagram of the system
2. A procedure showing how the fringes were captured, unwrapped and how was the 3D measurement was re-constructed
3. Details of the optimized three-frequency method that was adapted from reference 24.
4. A picture of the system test set-up. Figure 1 in the paper only shows the camera and projector in the system.
Other technical questions:
1. What is the limitation of the method? For example, any limitations on: size of the parts, slopes of the surfaces, continuity of the surfaces?
2. What are the advantages comparing with other similar technologies of 3D surface measurements, such as the reflectometry, the software configurable optical test system (SCOTS)?
Author Response
The comments are responsed in the file below.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper proposed a calibration approach to suppress phase error of fringe projection profilometry. The proposed method is based on the assumption "high success rate of phase unwrapping" and use an additional "auxiliary fringes" to obtain the optimal phase estimation. The experimental results are promising and able to support their claim. The paper is well prepared overall except few missing information. I would like to support the publication if the author can provide following information.
1. In page 6. Can the author explain why they capture the 28 auxiliary pictures in sequence? why they don't just project the patten shown in Fig 4 in one shot? Is any reason behind or just a practical issue?
2. A discussion on the limitation of using auxiliary fringe method is needed. how much cost on the system speed or response time for additional frame capture and processing compared with traditional means (such as LMS method mentioned in the paper).
Author Response
The comments are responsed in the file below.
Author Response File: Author Response.pdf
Reviewer 4 Report
The manuscript introduced an interference fringe-based phase reconstruction algorithm. Theoretical modelling was explained, and experiments were carried out. I have the following questions:
(1) In Fig. 5(a), what does the "phase samples in camera space mean"? Is the camera reading the phase directly in the design?
What does 1D plot of Fig. 5(a) look like? It seems 400 rad is 127pi. Does this show the phase of an interference pattern. It is not easy to read the 3D plot here.
(2) More details could be added to the experiment parts. How was FIg. 6(a) taken? What are the resolution of the camera image(pixels)? What are the center bright spot at the center of the two spheres?
In the cloud points plot in Fig. 6b, the diameter of the sphere is less than 20 mm, but the later table showed 30 mm. Why there was the discrepancy?
N/A
Author Response
The comments are responsed in the file below.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
This manuscript has been revised based on review’s comment. I think the manuscript can be accepted.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
1. In introduction:
The survey on the main technologies of 3D surface measurements was not precise. For example, the SCOTS technique can measure mirror and shinny surfaces as well. Please see the reference below. Also, it’s worth to compare with deflectometry technique.
Software configurable optical test system: A computerized reverse Hartmann test
August 2010, Applied Optics 49(23):4404-12
2. Figure 2, the schematic diagram and the context do not give enough details on how the surface (target) was calculated from three coordinates systems (camera, projector and target). This is in fact the key part of the paper.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
