Phase-shifted Sinusoidal Patterns Research Articles

Spectral refractive index assessment of turbid samples by combining spatial frequency near-infrared spectroscopy with Kramers–Kronig analysis

A practical algorithm for estimating the wavelength-dependent refractive index (RI) of a turbid sample in the spatial frequency domain with the aid of Kramers-Kronig (KK) relations is presented. In it, phase-shifted sinusoidal patterns (structured illumination) are serially projected at a high spatial frequency onto the sample surface (mouse scalp) at different near-infrared wavelengths while a camera mounted normally to the sample surface captures the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial absorption maps by logarithmic function, and once the absorption coefficient information is obtained, the imaginary part (k) of the complex RI (CRI), based on Maxell's equations, can be calculated. Using the data represented by k, the real part of the CRI (n) is then resolved by KK analysis. The wavelength dependence of n ( λ ) is then fitted separately using four standard dispersion models: Cornu, Cauchy, Conrady, and Sellmeier. In addition, three-dimensional surface-profile distribution of n is provided based on phase profilometry principles and a phase-unwrapping-based phase-derivative-variance algorithm. Experimental results demonstrate the capability of the proposed idea for sample's determination of a biological sample's RI value.

Structured-illumination reflectance imaging coupled with phase analysis techniques for surface profiling of apples

Three-dimensional (3-D) geometry information is valuable for fruit quality evaluation. This study was aimed at exploring an emerging structured-illumination reflectance imaging (SIRI) system, coupled with phase analysis, for reconstructing surface profiles of fruit. Phase-shifted sinusoidal patterns, distorted by the fruit geometry, were acquired and processed through phase demodulation, phase unwrapping and other post-processing procedures to obtain phase difference maps relative to the phase of a reference plane. The phase maps were then transformed into height profiles based on phase-to-height calibrations. A reference plane-based approach, in conjunction with the curve fitting technique using polynomials of order 3 or higher, was utilized for phase-to-height calibrations, which achieved superior accuracies with the root-mean-squared errors (RMSEs) of 0.027–0.033 mm for a height measurement range of 0–91 mm. The 3rd-order polynomial curve fitting technique was further tested on two reference blocks with known heights, resulting in relative errors of 3.75% and 4.16%. Tests of the calibrated system for reconstructing the surface of apple samples showed that surface concavities (i.e., stem/calyx regions) could be readily discriminated from bruising defects from both the phase difference images and reconstructed height profiles. This study has laid a foundation for using SIRI for reconstructing the 3-D geometry, and thus expanded the capability of the technique for quality evaluation of horticultural products. Further research is needed to utilize the phase analysis techniques for detecting surface concavities of apples, and optimize the phase demodulation and unwrapping algorithms for faster and more reliable detection.

A calibration method for non-overlapping cameras based on mirrored absolute phase target

Non-overlapping cameras are widely applied in visual measurement system and mobile robotics. The inspection accuracy and performance of the systems highly depend on the calibration accuracy. A novel method for the calibration of non-overlapping cameras is proposed in this paper. A LCD screen is used as a phase target to display two groups of orthogonal phase-shifted sinusoidal patterns during the calibration process. Through a mirror reflection, the phase target is captured by the cameras respectively. The relations between each camera and the phase target can be obtained according the proposed algorithm. Then, the relation between the cameras can be calculated by treating the phase target as an intermediate value. The proposed method is more flexible than a conventional mirror-based approach, because it does not require the common identification points and is robust to out-of-focus images. Both simulation work and experimental results show the proposed calibration method has a good result in calibrating a non-overlapping cameras system. The calibration accuracy can reach 0.2 mm and 0.007° in translations and rotation respectively. A stereo deflectometry system is calculated based on the proposed calibration method. The global measurement accuracy of a standard concave mirror measured by the system can reach 96.8 nm.

Determination of the complex refractive index segments of turbid sample with multispectral spatially modulated structured light and models approximation.

Spectral data enabling the derivation of a biological tissue sample's complex refractive index (CRI) can provide a range of valuable information in the clinical and research contexts. Specifically, changes in the CRI reflect alterations in tissue morphology and chemical composition, enabling its use as an optical marker during diagnosis and treatment. In the present work, we report a method for estimating the real and imaginary parts of the CRI of a biological sample using Kramers-Kronig (KK) relations in the spatial frequency domain. In this method, phase-shifted sinusoidal patterns at single high spatial frequency are serially projected onto the sample surface at different near-infrared wavelengths while a camera mounted normal to the sample surface acquires the reflected diffuse light. In the offline analysis pipeline, recorded images at each wavelength are converted to spatial phase maps using KK analysis and are then calibrated against phase-models derived from diffusion approximation. The amplitude of the reflected light, together with phase data, is then introduced into Fresnel equations to resolve both real and imaginary segments of the CRI at each wavelength. The technique was validated in tissue-mimicking phantoms with known optical parameters and in mouse models of ischemic injury and heat stress. Experimental data obtained indicate variations in the CRI among brain tissue suffering from injury. CRI fluctuations correlated with alterations in the scattering and absorption coefficients of the injured tissue are demonstrated. This technique for deriving dynamic changes in the CRI of tissue may be further developed as a clinical diagnostic tool and for biomedical research applications. To the best of our knowledge, this is the first report of the estimation of the spectral CRI of a mouse head following injury obtained in the spatial frequency domain.

A novel calibration method for arbitrary fringe projection profilometry system

A novel calibration method for phase-to-height (PTH) relationship in fringe projection profilometry (FPP) was proposed in this work. This proposed method can be applied to an FPP system of which the camera, projector and reference plane are positioned arbitrarily. First, a black-white pattern and four phase-shifted sinusoidal patterns are generated using a computer and projected onto the reference plane (ow-xw-yw coordinate plane) while being moved along its normal direction to several known positions. The camera records the projected fringe patterns on the reference plane at every position. Based on the projection principles of the camera and projector, unified phase values in this process were extracted enabling the PTH relationship to be determined easily. This makes the subtraction of a reference phase, as used in traditional FPP, is no longer necessary. Second, distorted fringe patterns reflected by target object are captured, and height values are calculated based on the obtained PTH relationship. Finally, by calibrating the intrinsic and extrinsic parameters of the camera, the 3D coordinates (xw,yw,zw) of object surface can be determined accordingly. The proposed method was verified by experiments, which demonstrate the validity and accuracy of the proposed method.

Development of a Multispectral Structured Illumination Reflectance Imaging (SIRI) System and Its Application to Bruise Detection of Apples

Abstract. SIRI is a promising new imaging modality for enhancing quality detection of food. A liquid-crystal tunable filter (LCTF)-based multispectral SIRI system was developed and used for selecting optimal wavebands to detect bruising in apples. Immediately after impact bruising, ‘Delicious’, ‘Royal Gala’, ‘Granny Smith’, and ‘Golden Delicious’ apples were imaged by the system over the spectral region of 650 to 950 nm with 20 nm increments under sinusoidally modulated illumination at a spatial frequency of 100 cycles m-1. Each sample was subjected to two phase-shifted sinusoidal patterns of illumination with phase offsets of 0 and 2p/3 that were generated by a digital light projector. For comparison, spectral images were also captured under conventional uniform illumination. Spiral phase transform, a newly developed two-phase based demodulation method, was then used to retrieve amplitude component (AC) and direct component (DC) images from the SIRI images, from which ratio images were obtained by dividing the AC images by the DC images. It was found that the uniform illumination images failed to reveal the bruises in apples, whereas bruises were distinctly visible in the ratio images, with contrast varying with wavelength. Principal component analysis (PCA) showed that seven wavelengths from 710 to 830 nm were more relevant to bruise detection. A modified Otsu thresholding method based on the between-class variance was proposed for bruise segmentation from the ratio images at each of the seven wavelengths as well as the first principal component (PC1) images, which resulted in overall detection errors of 11.7% to 14.2%. This study has shown the potential of using a multispectral SIRI system for defect detection of fruit. Further research is needed to develop a general algorithm for defect detection of apples and upgrade the system toward real-time detection. Keywords: Defects, Detection, Fruit, Image analysis, LCTF, Structured illumination.

Efficient single pixel imaging in Fourier space

Single pixel imaging (SPI) is a novel technique capturing 2D images using a bucket detector with a high signal-to-noise ratio, wide spectrum range and low cost. Conventional SPI projects random illumination patterns to randomly and uniformly sample the entire scene’s information. Determined by Nyquist sampling theory, SPI needs either numerous projections or high computation cost to reconstruct the target scene, especially for high-resolution cases. To address this issue, we propose an efficient single pixel imaging technique (eSPI), which instead projects sinusoidal patterns for importance sampling of the target scene’s spatial spectrum in Fourier space. Specifically, utilizing the centrosymmetric conjugation and sparsity priors of natural images’ spatial spectra, eSPI sequentially projects two -phase-shifted sinusoidal patterns to obtain each Fourier coefficient in the most informative spatial frequency bands. eSPI can reduce requisite patterns by two orders of magnitude compared to conventional SPI, which helps a lot for fast and high-resolution SPI.

Accuracy verification of infrared marker‐based dynamic tumor‐tracking irradiation using the gimbaled x‐ray head of the Vero4DRT (MHI‐TM2000)a)

To verify the accuracy of an infrared (IR) marker-based dynamic tumor-tracking irradiation system (IR tracking) using the gimbaled x-ray head of the Vero4DRT (MHI-TM2000). The gimbaled 6-MV C-band x-ray head of the Vero4DRT can swing along the pan-and-tilt direction to track a moving target. During beam delivery, the Vero4DRT predicts the future three-dimensional (3D) target position in real time using a correlation model [four-dimensional (4D) model] between the target and IR marker motion, and then continuously transfers the corresponding tracking orientation to the gimbaled x-ray head. The 4D-modeling error (E4DM) and the positional tracking error (EP) were defined as the difference between the predicted and measured positions of the target in 4D modeling and as the difference between the tracked and measured positions of the target during irradiation, respectively. For the clinical application of IR tracking, we assessed the relationship between E4DM and EP for three 1D sinusoidal (peak-to-peak amplitude [A]: 20-40 mm, breathing period [T]: 2-4 s), five 1D phase-shifted sinusoidal (A: 20 mm, T: 4 s, phase shift [τ]: 0.2-2 s), and six 3D patient respiratory patterns. The difference between the 95th percentile of the absolute EP (EP (95)) and the mean (μ) + two standard deviations (SD) of absolute E4DM (E4DM (μ+2SD)) was within ± 1 mm for all motion patterns. As the absolute correlation between the target and IR marker motions decreased from 1.0 to 0.1 for the 1D phase-shifted sinusoidal patterns, the E4DM (μ+2SD) and EP (95) increased linearly, from 0.4 to 3.0 mm (R = -0.98) and from 0.5 to 2.2 mm (R = -0.95), respectively. There was a strong positive correlation between E4DM (μ+2SD) and EP (95) in each direction [(lateral, craniocaudal, anteroposterior) = (0.99, 0.98, 1.00)], even for the 3D respiratory patterns; thus, EP (95) was readily estimated from E4DM (μ+2SD). Positional tracking errors correlated strongly with 4D-modeling errors in IR tracking. Thus, the accuracy of the 4D model must be verified before treatment, and margins are required to compensate for the 4D-modeling error.

초소형 카메라-프로젝터의 광학왜곡 보정을 이용한 위상변이 방식 3차원 스캐닝의 성능 향상

A distortion correction technique is presented to enhance the 3D scanning performance of a micro-size camera-projector system. Recently, several types of micro-size digital projectors and cameras are available. However, there have been few effort to develop a micro-size 3D scanning system. We develop a micro-sized 3D scanning system which is based on the structured light technique. Three images of phase-shifted sinusoidal patterns are projected, captured, and analyzed by the system to reconstruct 3D shapes of very small objects. To overcome inherent optical imperfection of the micro 3D sensor, we correct the vignetting and blooming effects which cause distortions in the phase image. Error analysis and 3D scanning results on small real objects are presented to show the performance of the developed 3D scanning system.