Calibration and Image Reconstruction in a Spot Scanning Detection System for Surface Defects

Round 1

Reviewer 1 Report

This paper proposes a calibration method for detection of surface defects in the spot scanning system. Calibration parameters are estimated by optimizing the constraint function. However, since the mapping function Eq.(7) from the surface coordinate to image one is not defined as a specific equation, the target constraint function Eq.(13) cannot be formulated specifically. So the implementability is unclear for readers. For the practical application, the mapping function Eq.(7) should be described as a specific formula including unknown parameters \psi to be estimated.

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Reviewer 2 Report

I found the paper very interesting and well written, it has been easy to follow the work. The use of English is good, but there are some grammatical errors that should be reviewed.  Both the abstract and the introduction are clear and describe the aim of the work and the basis of the research. The bibliographic references are numerous, up to date and well connected with the text, making it easy to find additional information. The mathematics that support the calibration method presented are consistent, and results show the usefulness of the proposed method.

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Reviewer 3 Report

This paper describes the calibration and image reconstruction method for a defect-detection system based on a spot-scanning and a rotational stage configuration. The system uses a scattered light detection using a parabolic mirror to enhance the photon collection efficiency. The calibration method here was successfully applied to calibrate the system, and it is useful for a general-purpose image reconstruction algorithm. I have several comments.

1. I understand that the authors ‘demonstrated’ the performance of the algorithm by doing a calibration procedure for a known pattern. However, if the x,y- coordinates for the rotation axis relative to the laser beam spot is known by other means, we do not need to use the image processing method to obtain the axis center coordinates. If applicable, the authors should use an alternative means to calibrate some of the parameters described here. 
2. The deviation from the ideal condition originates from the fact that the laser beam is irradiated at an angle. Thus the x,y coordinates of the spot shift depending on the thickness of the sample. If the laser beam is irradiated perpendicular to the stage, there is no need to consider the tilting of rotation axis and deviation of x,y, coordinates’ center position. Also, if a z-sample stage or a z-translator that moves the laser and the detection optics all together, were used, it can compensate for the sample’s known thickness. I think the authors are envisioning that the sample may not always be placed flat, and it may not be homogeneous thickness. If the specimen is thick and slanted, the algorithm introduced in this paper would be beneficial.
3. The center of rotation may be determined using a calibration wafer made of a simple radial pattern. I suppose that placing a standard size silicon wafer in the center of the stage should be done without any issue. Once we have the radial pattern rotated, the PMT signal should show periodic changes whenever the laser beam spot passes the lines. Using x,y- stages, if the laser beam spot is brought into the center of the rotation, PMT no longer sees the periodic changes.
4. At the constant rotation speed, the linear velocity varies at the outer edge of the stage versus location close to the center. At the outer edge, the spatial resolution (in microns) is lower than the spatial resolution near the center. Thus, discussing system resolution in pixels (unit) does not make sense. The system resolution need to be discussed in length scale.
5. As for the scan speed for finishing the entire sample, it looks like it would take about 74 minutes to complete the 127mmx127mm specimen. If one would use the averaging method as suggested, it will easily take 3~4 hours per sample. Is this an ideal speed for the application?
6. The advantage of the point scanner with the parabolic mirror detection over a camera-based system was not demonstrated in terms of increased detection sensitivity or increased spatial resolution. Considering a conventional ‘blue-ray disk (DVD) for movies’ having a spatial resolution of ~200 nm, I would think, in principle, the system described here should have a similar sub-micron spatial resolution. Perhaps, one could combine the whole wafer scan with the rotation (plus x-scan) stage, and a second scan with x,y- actuators only on a specific area of interest for a higher resolution image.
7. Related to (5) and (6), I would think a camera-based system would be faster to complete the inspection as it captures a million pixels in a fraction of time. For example, laser illumination can be done as a line scan using cylindrical lens and a galvo scanner. Structure illumination method (irradiating moving pattern of lines) is aslo used in a camera-based system.  If point scanning is necessary for higher sensitivity, optical scanning using a galvo-galvo scanner or resonant-galvo scanner would be faster compared to the ‘stage scanner’.  Related to these and (5), I suggest discussing scan speed (both total duration and scanning condition consideration (rotation speed etc..)) in the discussion section.
8. As for the PMT detection duration, one can go 100 ns, instead of 1 microsecond, especially if a sensitive PMT is used in a dark environment. Although the pixel resolution of the system was also defined by the speed of linear stage movement, a resolution and noise level may be improved by averaging signals captured by shorter PMT sampling duration.
9. I am wondering if the direct reflection light were collected with a polarizer and a silicon photosensor, one can reconstruct a structure image and subtract it from the scattered image to obtain an image of defects only. In addition, if a position-sensitive photodiode array (two segments or quadrant) were used at the reflection side, one can use it to calibrate the z-position shift due to sample thickness difference, and use it to correct z-axis shift using a z-stage. (Differential signal to identify z-shift, and total signal to construct reflection image).
10. Specifics of the rotation stage and the linear stages were not described. List manufacturer and model number if applicable. If they were custom made, mention that. These details are important for judging if the deviation from the ideal condition is related to the quality of stages used, or due to sample placement, or not well-configured (unfixed, mobile) optical system.

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Round 2

Reviewer 1 Report

In the revised version, a supplementary explanation was added, but it still lacks detail or specifics as seen in the sentence: "Since the specific expression is tediously long, we use to denote the mapping relationship for brevity." It seems that the additional explanation written in your response to Review 1, i.e., Step1 to Step 6, is preferable rather than the present sentence.

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