Photoacoustic Imaging (PAI) is a promising transcranial imaging technique for the mouse brain. However, the mouse skull imposes severe wavefront distortion to photoacoustic signals, thus reducing the quality of PAI. In this article, numerical simulations are implemented to study the influence of skull on PAI with respect to the distance of photoacoustic sources to skull. The k-Wave toolbox is adopted to simulate the photoacoustic wave propagation. The waveforms of shear and longitudinal waves within the skull layer are analyzed. Time reversal algorithm is applied to reconstruct the photoacoustic sources. Reconstruction results show that the mode conversion at the inner skull surface can cause streak artifacts around reconstructed point sources, and the artifacts are more obvious when the sources are near the skull. This study is expected to provide useful insights for transcranial photoacoustic imaging.
Spatial resolution is a critical measure of the imaging performance of ultrasound imaging systems and is determined by various system factors. So far, no comprehensive studies have been reported to elucidate the impact of system factors on spatial resolution, which is generally defined as the Full Width at Half Maximum (FWHM) of the Point Spread Function (PSF). This work aims to model the PSF of ultrasound imaging systems based on a linear transducer array and a Coherent Plane-Wave Compounding (CPWC) method and study how pulse-echo sequences, transducer parameters, and beamforming algorithms impact PSF. The Verasonics simulator and UltraSound ToolBox are used in numerical simulations for ultrasound signal generation and image reconstruction, respectively. Experiments are conducted to verify simulation results. Numerical and experimental results show that the value of axial resolution is negatively correlated with the center frequency of the ultrasonic transducer; the value of lateral resolution is positively correlated with the number of transmitted plane waves of the CPWC method and the element width of the ultrasonic transducer and is negatively correlated with the maximum steering angle of the CPWC method and the aperture size and center frequency of the ultrasonic transducer. Different beamforming algorithms show varying effects on spatial resolution and image quality. This work is expected to help predict and interpret the quality of ultrasound images produced by practical ultrasound imaging systems and is beneficial for the design and development of ultrasonic transducers, pulse-echo sequences, and beamforming algorithms for enhanced spatial resolution.
Photoacoustic computed tomography (PACT) is a rapidly developing biomedical imaging modality and has attracted substantial attention in recent years. Image reconstruction from photoacoustic projections plays a critical role in image formation in PACT. Here we review six major classes of image reconstruction approaches developed in the past three decades, including delay and sum, filtered back projection, series expansion, time reversal, iterative reconstruction, and deep-learning-based reconstruction. The principal ideas and implementations of the algorithms are summarized, and their reconstruction performances under different imaging scenarios are compared. Major challenges, future directions, and perspectives for the development of image reconstruction algorithms in PACT are also discussed. This review provides a self-contained reference guide for beginners and specialists in the photoacoustic community, to facilitate the development and application of novel photoacoustic image reconstruction algorithms.
High-speed imaging capability is essential for photoacoustic computed tomography (PACT) to monitor biological dynamics. The filtered back-projection (FBP) algorithm is widely-used in PACT for image reconstruction owing to its high computational efficiency. To achieve high-speed imaging, several acceleration strategies based on the graphics processing units (GPUs) have been proposed to further increase the computational efficiency of the FBP algorithm. However, there are few acceleration strategies reported based on the multi-core central processing units (CPUs). Considering the fact that multi-core CPUs are much more accessible than high-performance GPUs, here we report a multi-core CPU-based framework for enhancing the computational efficiency of the FBP algorithm. In this framework, the highly-parallel back-projection part of the FBP algorithm is programed with C++ and implemented in parallel with multi-core CPUs. In addition, the pre-calculation strategy is applied in this framework to avoid unnecessary repetitive computations. The results show that implementing the back-projection part in parallel with C++ can reduce the image reconstruction time by a factor of 2.4 compared with the conventional implementation in which the FBP algorithm is fully programed with MATLAB and executed in parallel with parfor. By applying the pre-calculation, the image reconstruction time is further reduced by a factor of 2.2. Overall, the proposed framework increases the computational efficiency of the FBP algorithm by a factor of 5.5 and only takes 0.04 seconds to reconstruct an image with 512 × 512 pixels. This work is expected to promote the development of high-performance PACT systems that feature high imaging speed without GPUs.
In photoacoustic tomography (PAT), image reconstruction refers to the formation process from photoacoustic signals to target images, which has an important influence on the image quality.At present, most reconstruction algorithms assume that the medium is homogeneous, which may cause distortion and artifacts in the reconstructed images. Therefore, considering the heterogeneity of the medium is important for accurate image reconstruction in PAT. The iterative reconstruction (IR) algorithm can incorporate the information of imaging system and media, and thus can provide high-quality image reconstruction. In this work, we investigate the IR algorithm in PAT with heterogeneous media based on point source response. We obtain the system matrix by calculating the photoacoustic signal of each point source in heterogeneous media based on the k-space pseudospectral method. The target image is reconstructed iteratively with the media information-coupled system matrix and the total variation (TV) regularization. We take a set of simulations to verify the effectiveness of the IR algorithm in heterogeneous media. The work provides a new method for accurate reconstruction of photoacoustic images.
In photoacoustic tomography (PAT), image reconstruction has a fundamental impact on image quality and imaging speed. Among various reconstruction algorithms, the analytical filtered back-projection (FBP) and the numerical time reversal (TR) algorithms are two commonly used image reconstruction techniques in PAT. However, so far, no comprehensive studies are reported on the comparisons of FBP and TR algorithms. In this work, we compare these two algorithms from the perspectives of computational efficiency, robustness to non-ideal detection surfaces, and applicability to heterogeneous media. The results show that: 1) In terms of computational efficiency, FBP is typically faster than TR due to its flexibility in the selection of the reconstruction region. 2) For non-ideal detection surfaces-based reconstruction, FBP can provide more accurate amplitude information for the limited-view reconstruction and can produce fewer image artifacts for the sparse-view reconstruction. 3) For acoustically heterogeneous media, the TR algorithm can incorporate acoustic properties and thus can yield high-quality images, while FBP fails in this case. This study can help researchers gain a deeper understanding of the FBP and TR algorithms and is expected to provide a guide for the reasonable selection of PAT image reconstruction algorithms.
Photoacoustic computed tomography (PACT) is an emerging hybrid imaging modality which can noninvasively reconstruct high-resolution and high-contrast images in deep tissues. However, due to the presence of acoustic heterogeneities within biological tissues, most existing image reconstruction algorithms based on the assumption of constant speed of sound (SOS) will cause image artifacts and distortions. In this paper, to account for the effects of acoustic heterogeneity in PACT image reconstruction, we introduce ultrasound computed tomography (USCT) to provide detailed SOS distribution of the biological tissues and coupling media. Numerical simulation shows that if the variation of SOS is small enough, image reconstruction algorithm with a constant SOS assumption could produce visually acceptable results; otherwise, significant image artifacts and distortions would appear. While with the aid of USCT, image artifacts induced by acoustic heterogeneity in PACT would be effectively suppressed. Since image artifacts and distortions are common image quality degradation factors in PACT, the proposed technique is expected to expedite the development of high-performance imaging, which is essential for widespread applications of PACT.
Photoacoustic tomography (PAT) is a fast-evolving biomedical imaging modality in recent years, which has unique applications in a range of biomedical fields. In PAT, image reconstruction is a critical step to produce high-quality optical absorption images from photoacoustic projections. To date, algorithms based on back projection are the most widely used image reconstruction techniques due to their simplicity and computational efficiency. However, images reconstructed by back projection contain negative intensities, which have no physical meanings and are essentially undesired artifacts. Here we study the formation mechanism, fundamental causes of the negativity artifacts in backprojection based PAT. Results show that limited detector bandwidth and limited view angle are two fundamental causes of the negativity artifacts. When the bandwidth of the detector is limited, back-projection signals will be distorted due to the loss of frequency contents and negativity artifacts thus occur. When the view angle of the detector is limited, photoacoustic signals propagating in three-dimensional space cannot be captured completely, resulting in negativity artifacts. This work provides a comprehensive understanding of the characteristics of negativity artifacts, which may promote the development of artifact-free image reconstruction algorithms.
The current study investigates the beneficial combination of optical coherence tomography (OCT) and photoacoustic microscopy (PAM) as a safe method for observing retinal and choroidal vasculature. A recent addition to the field has been the integration of gold nanoparticles (AuNPs) to provide enhanced contrast in OCT and PAM images. The improved analysis of capillaries is the result of the strong optical scattering and optical absorption of gold nanoparticles due to surface plasmon resonance. Femtosecond laser ablation created the ultra-pure colloidal gold nanoparticles, which were then capped with polyethylene glycol (PEG). The AuNPs were administered to thirteen New Zealand rabbits to determine the advantages of this technology, while also investigating the safety and biocompatibility. The study determines that the synthesized PEG-AuNPs (20.0 ± 1.5 nm) were beneficial in enhancing contrast in PAM and OCT images without demonstrating cytotoxic effects to bovine retinal endothelial cells. In living rabbits, the administered PEG-AuNPs resulted in an 82% increased signal for PAM and a 45% increased signal for OCT in the retinal and choroidal vessels. A histology and biodistribution report determined that the AuNPs had mostly accumulated in the liver and spleen. TUNEL staining and histology established that no cell injury or death in the lung, liver, kidney, spleen, heart, or eyes had occurred up to 1 week after receiving a dose of AuNP. The nanoparticle technology, therefore, provides an effective and safe method to enhance contrast in ocular imaging, resulting in improved visualization of retinal microvasculature.
Most reported photoacoustic ocular imaging work to date uses small animals, such as mice and rats, the eyes of which are small and less than one-third the size of a human eye, which poses a challenge for clinical translation. Here we achieved chorioretinal imaging of larger animals, i.e. rabbits, using a dual-modality photoacoustic microscopy (PAM) and optical coherence tomography (OCT) system. Preliminary experimental results in living rabbits demonstrate that the PAM can noninvasively visualize depth-resolved retinal and choroidal vessels using a safe laser exposure dose; and the OCT can finely distinguish different retinal layers, the choroid, and the sclera. This reported work might be a major step forward in clinical translation of photoacoustic microscopy.
Current clinical available retinal imaging techniques have limitations, including limited depth of penetration or requirement for the invasive injection of exogenous contrast agents. Here, we developed a novel multimodal imaging system for high-speed, high-resolution retinal imaging of larger animals, such as rabbits. The system integrates three state-of-the-art imaging modalities, including photoacoustic microscopy (PAM), optical coherence tomography (OCT), and fluorescence microscopy (FM). In vivo experimental results of rabbit eyes show that the PAM is able to visualize laser-induced retinal burns and distinguish individual eye blood vessels using a laser exposure dose of ~80 nJ, which is well below the American National Standards Institute (ANSI) safety limit 160 nJ. The OCT can discern different retinal layers and visualize laser burns and choroidal detachments. The novel multi-modal imaging platform holds great promise in ophthalmic imaging.
We propose a simple yet effective phase demodulation algorithm for two-shot fringe patterns with random phase shifts.
The phase to be recovered is decomposed into a linear combination of finite terms of orthogonal polynomials; the
expansion coefficients and the phase shift are exhaustively searched through global optimization. The technique is
insensitive to noise or defects, and is capable of retrieving phase from low fringe-number interferograms. The retrieved
phase is continuous and no further phase unwrapping process is required. The method is expected to be promising to
process interferograms with regular fringes.
Standard phase-shifting interferometry (PSI) generally requires collecting at least three phase-shifted interferograms to
extract the physical quantity being measured. Here, we propose a simple two-frame PSI for the testing of a range of
optical surfaces, including flats, spheres, and aspheres. The two-frame PSI extracts modulated phase from two randomly
phase-shifted interferograms using a Gram-Schmidt algorithm, and can work in either null testing or non-null testing
modes. Experimental results of a paraboloidal mirror suggest that the two-frame PSI can achieve comparable
measurement precision with conventional multi-frame PSI, but has the advantages of faster data acquisition speed and
less stringent hardware requirements. It effectively expands the flexibility of conventional PSI and holds great potential
in many applications.
Photoacoustic tomography (PAT) provides a unique tool to diagnose inflammatory arthritis. However, the specificity and sensitivity of PAT based on endogenous contrasts is limited. The development of contrast enhanced PAT imaging modalities in combination with small molecule contrast agents could lead to improvements in diagnosis and treatment of joint disease. Accordingly, we adapted and tested a PAT clinical imaging system for imaging the human joints, in combination with a novel PAT contrast agent derived from an FDA-approved small molecule drug. Imaging results based on a photoacoustic and ultrasound (PA/US) dual-modality system revealed that this contrast-enhanced PAT imaging system may offer additional information beyond single-modality PA or US imaging system, for the imaging, diagnosis and assessment of inflammatory arthritis.
Non-alcoholic fatty liver disease (NAFLD) is a common liver disease affecting 30% of the population in the United States. Biopsy is the gold standard for diagnosing NAFLD. Liver histology assesses the amount of fat, and determines type and extent of cell injury, inflammation and fibrosis. However, liver biopsy is invasive and is limited by sampling error. Current radiological diagnostic modalities can evaluate the 'physical' morphology in liver by quantifying the backscattered US signals, but cannot interrogate the 'histochemical' components forming these backscatterers. For example, ultrasound (US) imaging can detect the presence of fat but cannot differentiate steatosis alone from steatohepatitis. Our previous study of photoacoustic physiochemical analysis (PAPCA) has demonstrated that this method can characterize the histological changes in livers during the progression of NAFLD in animal models. In this study, we will further validate PAPCA with human livers. Ex vivo human liver samples with steatosis, fibrosis and cirrhosis will be scanned using optical illumination at wavelengths of 680-1700 nm and compared to histology results. In vivo study on human subjects with confirmed steatosis is planned using our PA-ultrasound (US) parallel imaging system based on Verasonic US imaging flatform with an L7-4 probe. 10 mJ/cm2 per pulse optical energy at 755 nm will be delivered to the skin surface, which is under the safety limit of American National Standard Institute. Preliminary study with ex vivo human tissue has demonstrated the potential of the proposed approach in differentiating human liver conditions.
Gold nanoparticles (AuNPs) have been extensively explored as a model nanostructure in nanomedicine and have been widely used to provide advanced biomedical research tools in diagnostic imaging and therapy. Due to the necessity of targeting AuNPs to individual cells, evaluation and visualization of AuNPs in the cellular level is critical to fully understand their interaction with cellular environment. Currently imaging technologies, such as fluorescence microscopy and transmission electron microscopy all have advantages and disadvantages. In this paper, we synthesized AuNPs by femtosecond pulsed laser ablation, modified their surface chemistry through sequential bioconjugation, and targeted the functionalized AuNPs with individual cancer cells. Based on their high optical absorption contrast, we developed a novel, label-free imaging method to evaluate and visualize intracellular AuNPs using photoacoustic microscopy (PAM). Preliminary study shows that the PAM imaging technique is capable of imaging cellular uptake of AuNPs in vivo at single-cell resolution, which provide an important tool for the study of AuNPs in nanomedicine.
We developed a simple and effective contrast for tissue characterization based on the recently proposed dual-pulse nonlinear photoacoustic technology. The new contrast takes advantage of the temperature dependence of Grüneisen parameter of tissue and involves a dual-pulse laser excitation process. A short pulse first heats the sample and causes a temperature jump, which then leads to the change of Grüneisen parameter and amplitude of the photoacoustic signal of the second pulse. For different tissues, the induced rate or trend of change is expected to be different, which constitutes the basis of the new contrast. Preliminary phantom experiment in blood and lipid mixtures and in vitro experiment in fatty rat liver have demonstrated that the proposed contrast has the capability of fast characterization of lipid-rich and blood-rich tissues.
The feasibility of an innovative biomedical diagnostic technique, thermal photoacoustic (TPA) measurement, for nonionizing and non-invasive assessment of bone health is investigated. Unlike conventional photoacoustic PA methods which are mostly focused on the measurement of absolute signal intensity, TPA targets the change in PA signal intensity as a function of the sample temperature, i.e. the temperature dependent Grueneisen parameter which is closely relevant to the chemical and molecular properties in the sample. Based on the differentiation measurement, the results from TPA technique is less susceptible to the variations associated with sample and system, and could be quantified with improved accurately. Due to the fact that the PA signal intensity from organic components such as blood changes faster than that from non-organic mineral under the same modulation of temperature, TPA measurement is able to objectively evaluate bone mineral density (BMD) and its loss as a result of osteoporosis. In an experiment on well established rat models of bone loss and preservation, PA measurements of rat tibia bones were conducted over a temperature range from 370 C to 440 C. The slope of PA signal intensity verses temperature was quantified for each specimen. The comparison among three groups of specimens with different BMD shows that bones with lower BMD have higher slopes, demonstrating the potential of the proposed TPA technique in future clinical management of osteoporosis.
For three-dimensional imaging of optical absorbance, the existing technology of photoacoustic microscopy (PAM) has quite poor axial resolution, the tens of microns to hundreds of microns. This is despite the fact that PAM has recently achieved lateral resolutions on the order of a micron or submicron, comparable to that of optical microscopy. In this paper, a pure optical photoacoustic microscopy (POPAM) with optical rastering of a focused excitation beam and optically sensing of the photoacoustic signal using a microring resonator was developed with the super broad bandwidth of the system more than 350MHz. With unprecedented broad bandwidth of POPAM, 3.8μm axial resolution was achieved without deconvolution processing. Sectioning imaging ability along axial direction presenting 3D morphologic features was shown based on imaging printed phantom. The impact of this approach will be similar to how confocal optical microscopy revolutionized the conventional optical microscopy by enabling the axial sectioning capability. Tissue imaging comparing POPAM and conventional PAM based on needle hydrophone demonstrated that though such broad bandwidth compromised the sensitivity of POPAM 4.35 times than that of conventional PAM, the noise equivalent detectable pressure (NEDP) was estimated as 74Pa, still able to get the tissue imaging.
The partial null interferometric aspheric testing technique, based on the Twyman-Green interferometer system, is very
useful and of good versatility. In this technique, the under-test aspheric needs to be located precisely. Taking advantage of ray tracing and digital image processing technique, a new method to locate aspheric is proposed. Firstly, model and simulate the Twyman-Green interferometer system in the ray tracing software ZEMAX, find an optimal test position and generate an optimal referenced interferogram. Record the interferogram and make it a target for the experimental interferogram to achieve. At the same time, an experimental interferogram can be obtained by building the same testing system experimentally. Process the one-dimensional gray scale data in X-axis of the two interferograms, two curves, indicating the black and white change of the interference fringes, are obtained. By comparing the normalized X coordinates of the peaks of the two curves, we can determine whether the under-test aspheric is positioned well. In order to locate the aspheric precisely, the aspheric has to be moved repeatedly to get a perfect interferogram whose peaks of interference fringes match well with those of the target interferogram. An experiment for testing a paraboloid with diameter 100mm and asphericity 50μm is carried out. The result shows that this kind of locating method has an Accuracy of 3-5μm, which demonstrates that the method is practicable and high-precision.
In this article, an interference digital testing method for measuring spatial density distribution of transmissive objects is
presented. This method applies a radial shearing interferometer to test the density field from 8 projections in the same
plane. By taking advantage of the regularized phase-tracking technique (RPT), the single interferogram will be
demodulated to two-dimensional phase distribution of the corresponding projection beam. Then the phase data on one
given cross-section of every projection is selected to form 8 curves, which describe one-dimensional phase variation on
the given cross-section from each projection. Regarding these curves as computer tomography projection data, the
refractive index distribution of the given cross-section can be reconstructed utilizing the algebraic reconstruction
technique (ART). Thus, a three-dimensional distribution of refractive index can be obtained by applying the method
above to different cross-sections in order. Finally, we are capable of calculating the spatial density distribution with the
relation between density and refractive index of the substance tested. In addition, the density field testing for hypersonic
flow field is investigated as an example in this article. Considering the fact that the target model in the optical window
center of a wind tunnel will inevitably block some testing beams, which will lead to the sharp decline in accuracy of the
testing results, a modified algebraic reconstruction technique which improves accuracy by introducing biharmonic
spline interpolation is presented. In simulation, an error less than 3% in non-block situation is reached while an error less
than 8% in small-area-block situation is also obtained.
A non-null aspheric testing system, which employs partial null lens (PNL for short) and reverse iterative optimization
reconstruction (ROR for short) technique, is proposed in this paper. Based on system modeling in ray tracing software,
the parameter of each optical element is optimized and this makes system modeling more precise. Systematic error of
non-null aspheric testing system is analyzed and can be categorized into two types, the error due to surface parameters of
PNL in the system modeling and the rest from non-null interferometer by the approach of error storage subtraction.
Experimental results show that, after systematic error is removed from testing result of non-null aspheric testing system,
the aspheric surface is precisely reconstructed by ROR technique and the consideration of systematic error greatly
increase the test accuracy of non-null aspheric testing system.
The radial shearing interferometer that is immune to vibration and the spatial phase modulation technique that can
retrieve the phase from a single interferogram can be used for precise measurement of aspheric surfaces. However, as a
carrier is needed to be introduced in the system to keep the fringes open, the spatial phase modulation technique
generally leads to a great increase in the density of the fringes. A novel method that uses just one frame of the
interferogram and need not introduce any spatial carrier in the interferometer is proposed in the paper. To demodulate the
closed interferograms generated in the system, a regularized phase-tracking technique that can be used for a single open
or closed fringe pattern is employed to recover the phase map. Actually the presented method can also be applied in
many other cases, for example flow visualization. Both computer simulation and experimental result have demonstrated
the validity and efficiency of the proposed method.
KEYWORDS: Aspheric lenses, Wavefronts, Interferometry, Sensors, Computer simulations, Beam splitters, Ray tracing, Digital cameras, Systems modeling, Nano opto mechanical systems
With respect to null test, non-null test is more flexible and can provide fast, general test with acceptable accuracy. A
non-null interferometric aspheric testing system, which employs partial null lens and reverse optimization
reconstruction, is proposed. The partial null lens compensates most of the longitude aberration of the aspheric under test
and keeps the slope of the non-null wavefront within the resolution of the detector. The reverse optimization
reconstruction procedure reduces the retrace error of the non-null test and reconstructs the figure of the test aspheric. The
characteristic, design process of the partial null lens and especially the implement of the reverse optimization
reconstruction are discussed in detail. Computer simulation shows the reverse optimization reconstruction procedure can
reconstruct the aspheric figure error with an accuracy better than 1/200wave within 5 mins. The error analysis is also
considered and some conclusions are given. This research is of great importance for general aspheric surfacing and testing.
Based on the difference between theoretical with real interferogram images the figure of original aspheric surface can be
obtained using an algorithm of Reverse iterate Optimization Reconstruction (ROR) calculating technique. Because the
procedure of ray tracing path needed an accurate geometry of optical structure size so the aspheric and compensator LC must be located in the optical path. To avoid the compensator LC resulted in bigger spherical aberration a smart located method is proposed in this paper. Before measurement an aplanatic lens consists of compensator LC and another
removable lens LM that the last surface is a standard one. So Fiezau interference is formed by the standard one with reflected ray from the vertex of aspheric that the aspheric surface detected can be accurately located. At testing the
lenses LM will be removed and the aspheric is moved to an adapted position. The experiments show the displacement locating accuracy is an amount of micron. The RMS for aspheric testing of ROR calculating technique is better than 1/200 wavelength.
Aspheric design and fabrication have obtained great achievements with the fast developments of modern science and technology, especially computer science, while the test of aspherics has become a chief limitation of aspheric applications. Due to the arbitrary nature of aspherics, test of all aspherics with only one instrument seems impossible. This paper presents a non-null interferometric system that can be applied for general aspheric test. The systematic error of non-null aspheric test system is studied, according to which an error separating and correcting method is proposed then. Computer simulation shows the error correcting method can correct the systematic error of non-null aspheric test system effectively and efficiently. Experiments have been carried out with the proposed interferometric non-null aspheric test system and the results show the system can greatly increase the accuracy of the non-null aspheric test.
Bicycle lamp used for road lighting is becoming popular now. However, few people have realized its potential market
and correlative researches are far from enough. Generally speaking, researches on bicycle lamps are mostly focused on
how to design a reflector which will collect light energy more efficiently and can transfer it to certain areas forward
when the light source is determinated. In traditional angle of view, the reflector is usually a paraboloid or ellipsoid.
However, both of them can not meet the requirement in practice most of the cases. Therefore, free form reflectors (FFRs)
instead are widely used. In this paper, a new approach to design FFR which is convenient and rapid is presented. To do
computer-aided simulation, certain light source should be selected first. Usually, light sources that behavior like a
Lambertian emitter are modeled. To examine the correctness of this approach, a bicycle lamp is designed according to
this approach to see if it can meet the requirements of the Germany standard which will be introduced in the text later.
The standard requires specific illuminance values for particular points at the test screen with a distance of 10m from the
source. The simulation results is exciting and can meet all the requirement. For example, 10lx is expected at the point (0,
0) while the obtained value is 10.42lx, under the conditions that the total luminous flux of the light source is 42lm and
the reflectivity of FFR is 0.8. This method has certain universal significance and can provide references for the design of
other illumination systems.
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