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It is important to ensure the security of biometric authentication information, because its leakage causes serious risks, such as replay attacks using the stolen biometric data, and also because it is almost impossible to replace raw biometric information. In this paper, we propose a secure biometric authentication scheme that protects such information by employing an optical data ciphering technique based on compressed sensing. The proposed scheme is based on two-factor authentication, the biometric information being supplemented by secret information that is used as a random seed for a cipher key. In this scheme, a biometric image is optically encrypted at the time of image capture, and a pair of restored biometric images for enrollment and verification are verified in the authentication server. If any of the biometric information is exposed to risk, it can be reenrolled by changing the secret information. Through numerical experiments, we confirm that finger vein images can be restored from the compressed sensing measurement data. We also present results that verify the accuracy of the scheme.

Hybrid-resolution multispectral imaging is a framework to acquire multispectral images through a reconstruction procedure using two types of measurement data with different spatial and spectral resolutions. In this paper, we propose a new method for such a framework on the basis of a full-resolution RGB image and the data obtained from an image sensor with a multispectral filter array (MSFA). In the proposed method, a small region of each image band is reconstructed as a linear combination of RGB images, where the weighting coefficients are determined using MSFA data. The effectiveness of the proposed approach is shown by simulations using spectral images of natural scenes.

This paper proposes a class-based spectral estimation method for high-resolution red, green, and blue (RGB) images and corresponding low-resolution spectral data. Each spectrum in the low-resolution data is assumed to be a mixture of spectra of different classes. Then, the spectral estimation matrix for every class is derived using a regression approach, in which the clustering results of the high-resolution RGB image are used to incorporate spectral unmixing. Experiments confirm reduced normalized root mean squared error for the spectral images if the number of classes in the clustering is appropriately selected. In addition, the experimental results show that the spectra are accurately reconstructed even when they are observed as mixed spectra in the low-resolution data.

We have shown that the application of double random phase encoding (DRPE) to biometrics enables the use of biometrics as cipher keys for binary data encryption. However, DRPE is reported to be vulnerable to known-plaintext attacks (KPAs) using a phase recovery algorithm. In this study, we investigated the vulnerability of DRPE using fingerprints as cipher keys to the KPAs. By means of computational experiments, we estimated the encryption key and restored the fingerprint image using the estimated key. Further, we propose a method for avoiding the KPA on the DRPE that employs the phase retrieval algorithm. The proposed method makes the amplitude component of the encrypted image constant in order to prevent the amplitude component of the encrypted image from being used as a clue for phase retrieval. Computational experiments showed that the proposed method not only avoids revealing the cipher key and the fingerprint but also serves as a sufficiently accurate verification system.

We are currently developing an imaging system that combines simultaneous positron emission tomography (PET) with near-infrared (NIR) optical tomography, thus supporting two different types of molecular imaging. For this system, we are considering whether to use depth of interaction (DOI) PET detectors as simultaneous detectors of gamma rays and NIR light by changing the original upper reflectors to dichroic mirrors. The DOI-PET detector has very low spatial resolution for NIR light compared to the charge-coupled device cameras that are normally used. However, it is possible to reconstruct images of comparable value from the data acquired by low-resolution devices because the light is scattered by biological tissues and high-resolution devices are not necessarily effective at improving image quality. In this study, we demonstrate the feasibility of 3D NIR fluorescence tomography imaging by employing DOI-PET detectors in computer simulations. In the simulations, we used a 40 mm x 40 mm x 40 mm cubic phantom, a square detector geometry, and an optical diffusion equation to approximate the light propagation. We then evaluated imaging systems for 3D fluorescence tomography with different detector resolutions and excitation light arrangements using singular-value analysis and imaging simulation. We confirmed that the reconstructed images from low-resolution detectors (8 x 8 pixels for an area of 40 mm x 40 mm) are the same as those from high-resolution detectors (16 x 16 pixels for the same area).

This study proposes a piecewise Wiener estimation method to reconstruct a spectral reflectance image from a three-band image by multipoint spectral information collected simultaneously with image acquisition. A three-band image is divided into several blocks and the spectral estimation is carried out using the Wiener estimation matrix assigned to each block. Each Wiener estimation matrix is constructed on the basis of spectral measurement data. The experimental results show that the proposed method reduces the average estimation error monotonically as the number of spectral measurements increases. In addition, the computational time of the piecewise Wiener estimation costs only severalfold of the computational time of the conventional single-matrix method.

We made a tissue phantom with double-peak particle size distribution, which has polystyrene particles of cell nuclear size and mitochondrial size, and measured the spectrum from the tissue phantom using a single optical fiber. In this paper we investigate the characterization method for the tissue phantom with double-peak particle size distribution by comparing the measured spectra with the calculated ones using the Monte Carlo (MC) method. It is first shown that the Mie phase function characterizes better than the Henyey-Greenstein (H-G) phase function in MC calculation. Next, we compare the measurement spectra with those obtained by modeling as single-peak, conventional modeling for particle size distribution, and for double-peak particle size distribution. The single-peak modeling is found to cause considerable error for the tissue phantom with double-peak particle size distribution, which seems to simulate a biological tissue. We suggest that if one simulates the particle size distribution of a biological tissue by conventional modeling, the accuracy of estimation will be lower.

We propose a new illumination method for a medical endoscope: narrow band imaging (NBI), in which the spectral bandwidth of the filtered light is narrowed. To confirm how the spectral specifications of the filtered light influence a reproduced image, an experiment was conducted observing the endoscopic images of the back mucosa of a human tongue. In addition, the effect of NBI on endoscopic images was investigated through preliminary clinical tests in colonoscopy and upper gastrointestinal endoscopy. It has been shown that NBI can enhance the capillary pattern and the crypt pattern on the mucosa. These patterns are useful features for diagnosing an early cancer.

A method for estimating a spectral reflectance image of an object is presented, in which the image of a color chart is used instead of the spectral characteristics of the camera and the illumination. Since the spectral characteristics of the color chart are the essential issue in this method, this paper shows the requirement for the color chart based on the spectral characteristics of the set of target objects. Computer simulations are performed to confirm the effectiveness of the proposed method for typical multi-band imaging systems and illuminations. In addition, an investigation is carried out to roughly estimate the amount of the error when the color chart does not satisfy the requirement completely.

A method to reproduce images of an object under various observation conditions is presented. In this method, a series of multispectral images is captured by rotating the object under a point light source of which spectral power distribution and the position are known. The captured images are decomposed into diffuse and specular reflection component images based on the dichromatic reflection and the Lambertian models. Next, the incident angle of the illumination light and the angle between viewing direction and regular reflection are calculated based on observation geometry. Finally, the image under observation geometry is synthesized using the light-ray rearrangement technique. The experiments are carried out using two-dimensional objects, leather and fabric. Most of the synthesized images are shown to be the same as the images actually captured under the assumed illumination geometry, even if the object has complex reflection like fabric for which it is difficult to apply the reflection model used in computer graphics.

To reproduce the natural color of an object through color im- aging systems, the range of the reproducible color, i.e., the color gamut, of the color display devices must be expanded, because the color gamut of current display devices such as cathode ray tubes (CRTs) and liquid crystal displays (LCDs) is insufficient. We present a new method to en- large the color gamut for the LCD device using more than three prima- ries, i.e., multiprimaries, generated by a diffraction grating and a liquid crystal panel. The optical system for the multiprimary color display is introduced, and its capability of increasing the gamut is discussed. The experimental result displayed by seven primary colors is also demon- strated. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)02011-5)

Using scattered radiation as useful information to improve radioisotope image quality is a topic attracting many researchers. Some reports showed that incorporating scattered components offers a possibility to improve image quality. The general method is modeling scatter in multiple energy windows and incorporating that information into the reconstruction process. However, what the performance will be and how noise will behave when using scattered radiation in reconstruction are not yet well answered. In this paper, we investigate a method of modeling scatter in multiple energy windows in cases of a few projection views. The system performance is analyzed using singular value decomposition and resolution kernels. For noise behavior investigation, reconstructions are accomplished by estimating the variance of reconstructed voxel values and the effectiveness of using scatter is evaluated by resolution kernel analysis. The results show there are improvements in normalized mean-square error of the images and the resolution kernels. When photon counts fall below about one million, it is still effective to use scatter for some cases of a few projections

A 3D imaging system using a double-axis fluorescence microscope provides a practical way to reconstruct 3D images of micro-objects from images simultaneously acquired from the two orthogonal directions. In this paper, we show experimental results of 3D image reconstruction using a water plant specimen as an object.

In contrast to a conventional optical matched filtering system, which converts scalar information of objects into an intensity distribution of coherent light using the so-called incoherent-coherent converter, a new matched filtering system that uses a complex amplitude modulation device and a reference wave is proposed in this paper. As a concrete example to show the necessity of complex amplitude modulation, color image discrimination by the proposed optical system is shown and its validity is experimentally confirmed.

We propose a 3D computed tomography method based on the generalized Radon transform defined for incoherent optical systems. We apply this method to reconstruct microscopic 3D images efficiently from 2D images acquired with multi-axis fluorescence microscopes which eliminate missing frequency bands. Simulation results based on digital algorithms are shown.

An image restoration based on a color synthesis method is applied to the color imaging system by the lens with chromatic aberration. Using the continuous-discrete model in which spatial and spectral distribution of the object is considered continuously, the color imaging system with chromatic aberration is mathematically modeled and the technique of reconstructing an arbitrary color band image from the observed color images is present. Moreover, the focus adjustment can be done after the capture of the image by using the proposed imaging system.

The object’s surface structure can be obtained from an image sequence taken through a conventional CCD endoscope. This paper reports clinical experimental results of the method. The accuracy of the estimation is studied and a method to estimate the reliability of the reconstructed shape is also described.

We propose a new method to measure surface topography using a monocular endoscope. The surface structure is obtained up to a scale factor from an image sequence taken through a conventional CCD endoscope. The scale factor is determined by a photometric method, and the actual size of the object can be determined. The principle and experimental results are presented.

A new CGH (computer generated hologram) common path interferometer, which can be used for testing an aspherical mirror with large aperture, is proposed. This interferometer does not have a circle of least confusion, and a spatial filter can be used effectively to stop extraneous lights so that interferograms with good contrast can be obtained. The phase shifting technique can be easily applied to the interferometer. The method of designing and making the CGH zone-plate is described.

We analyze the influence of error in the measurement of shear value, which is a major source of error in tested results by the lateral shearing interferometer. A novel method is proposed for accurately measuring the shear of this interferometer. By introducing a defocused wavefront and making use of the wavefront slope data of the defocus and the parameters of the interferometer, we can calculate the shear value precisely, with an error less than the sampling interval of the detector. An experiment was conducted to show the effectiveness of the method.

In previous research we developed anoptical model to visualize volumetric arrays of data. In this paper we propose to implement the optical model in a hybrid system, and present some results obtained in the experimental stage. Through the experiment we found out that the computing time required to visualize three dimensional arrays of data using the hybrid system is notably reduced and that operations like rotation, interpolation, zooming and masking the whole volume data, do not require any extra computing time. The results presented in this paper were obtained for a particular case of the optical model, where the optical constant was the refractive index.

An approach is proposed to estimate an object's surface topography from monocular endoscopic images. In this approach the relative movement between the object and the endoscope is used for the estimation. After detecting disparities between images, the relative movement and the surface topography are sequentially estimated. Experimental results obtained with the method are also presented.

A 3D optical imaging method is presented based on computed tomography techniques. The 3D optical transfer function of our system has a higher band spherically, since 3D reconstructed images are composed only of the in-focused information of objects. Experimental results are shown for a simulated fluorescence microscope.

We propose a method to produce a hard copy of a three-dimensional (3-D) image by a conventional high-resolution printer. Parallax information is recorded on a transparency by the printer, and a reflection-type holographic screen composed of a number of small elementary holograms is attached on the transparency. The quality of the 3-D image is investigated, and the characteristics of the proposed method are described. 3-D image of full-parallax is experimentally produced using a laser printer.

A new method for rainbow and multicolor holographic stereograms is described using the technique of multidot recording, which was originally developed for the syntheses of full-parallax holographic stereograms. Instead of recording vertical parallax, an image of horizontal slit is synthesized for rainbow holography. It becomes possible to obtain large images by a compact optical system, since the hologram is composed of many small elementary holograms. Multicolor image is also produced by the same system introducing a simple image processing. Experimental results of three-dimensional and color imagery are demonstrated.

The objective of this paper is to develop a method which reconstructs coronary arteries in three dimensions from the small number of projections obtained from venography. Because this reconstruction problem is strongly ill-conditioned, a method, which used simulated annealing and introduced constraints such as the density range and the blood vessel continuity, was proposed in the previous paper. In this paper, a modified cost function is proposed, which leads to a better image, and experimental results are presented. A phantom which consists of heart and coronary arteries was used in the experiment, and heart and coronary arteries were successfully reconstructed. Furthermore, experimental results also show that the reconstructed image preserves important information for a medical examination such as the shape and the absorption coefficients of blood vessels.

We propose a holographic three-dimensional (3-D) printer that produces 3-D hard copies of computer data. A new technique for synthesizing a holographic stereogram (HS) has been invented for the purpose of making accurate hard copies of 3-D objects. The flat-format, Lippmann-type HS is printed by one optical step and is ideally suitable for 3-D printer application. This type of HS has both horizontal and vertical parallaxes so that the reconstructed image is free from distortion. The principle and the image quality of this type of HS are described, and a reconstructed image from this type of HS with 160 × 128 elements is experimentally demonstrated. The systematic constitution of a holographic 3-D printer is also discussed.

When simulated annealing is applied to an ill-posed reconstruction of computer tomography images, the cost function should be appropriately modified to suppress artifacts arising from the ambiguity of null components. This paper shows such modification of the cost function and proves its performance through singular value decomposition analysis. Computer simulation shows good agreement with the analysis.

Three-dimensional reconstruction of a bone image is important in medicine to facilitate making artificial bones by numerical control and to achieve computer simulations of surgical operations. Instead of gathering sectional tomograms obtained by computer tomography, a direct 3-D reconstruction, which is much better in terms of higher spatial resolution and smaller X-ray dosage, is used to extract the bone's shape. A proposal and an experimental result are presented in this paper.

A radial shearing interferometer with two equispaced circular gratings is described for obtaining a constant radial displacement of the test wavefront. The procedure for the fringe analysis is shown by applying the Fourier transform method to the circular fringe pattern for precisely obtaining the differentiation of the test wavefront. A novel method is also shown for holographically making the equispaced circular gratings by using a cylindrical mirror and a collimating lens. It is shown that the deflection and misalignment of the gratings will not appear in the interferogram by using the holographic production method.

We analyzed the distribution of the key-space in the phase-only DRPE by means of calculating a Euclidean distance between the decryption key and the encryption key and counting the number of the correct decryption keys.

In this paper we propose a general model for the visualization of the 3D volume data, called optical model (OM). We present the model in its most general form, and a particular case is used for the display of computed tomography (CT) data. The optical model contains some of the techniques available in the literature as particular cases. It does not use ray tracing however it uses the wave characteristics of the light. Using Maxwell's equations and the boundary conditions, the equations involved in the visualization process take a simple form. The optical model proposes to use such optical concepts as reflection, transmission, diffusion, absorption, or a combination of them for the visualization of the volume data. This new model uses the normalized gradient as the normal to the surface where diffusion takes place. In the optical model the optical constants involved in the calculations are directly mapped from the original 3D volume data. The optical model is addressed to display any kind of 3D volume data, however we only applied it in the visualization of CT data, as a particular example.

We propose a new image processing method which enables the use of a single lens instead of an automatic focusing system in the electronic still camera. The simulated annealing algorithm is applied to restoration of space-variant image blur, and an electroptic hybrid processor with the optics equivalent to the imaging system is also proposed for a hardware implementation of simulated annealing. Numerical estimations of the imaging parameters are not required, and highly parallel processing is possible. We also describe a method capable of gray-level data with low dynamic-range devices. Results from experiments and a computer simulation are presented.

We propose a new method for the automatic printing of holographic three-dimensional (3-D) animation viewed under white-light illumination. One can display the animated 3-D image near the hologram plane by vertically scrolling the hologram. Since the hologram consists of small elemental holograms that are individually recorded at multiple exposures, the image size and the playback length are not restricted by the size of the recording optical system. A 3-D animation of 25 frames is experimentally recorded. Clear 3-D images can be observed by pulsed-light illumination.

We proposed a smart card holder authentication system that combines fingerprint verification with PIN verification by applying a double random phase encoding scheme. In this system, the probability of accurate verification of an authorized individual reduces when the fingerprint is shifted significantly. In this paper, a review of the proposed system is presented and preprocessing for improving the false rejection rate is proposed. In the proposed method, the position difference between two fingerprint images is estimated by using an optimized template for core detection. When the estimated difference exceeds the permissible level, the user inputs the fingerprint again. The effectiveness of the proposed method is confirmed by a computational experiment; its results show that the false rejection rate is improved.

It is possible to capture images with high-fidelity color by using a spectrum-based color image reproduction method that estimates the spectral information of objects from a multispectral image along with information from illumination. When multispectral images do not have a sufficient signal-to-noise ratio (SNR), the accuracy of the spectral and color estimation will be reduced. To improve color estimation accuracy, this paper proposes a spatio-spectral Wiener estimation, which uses spatial correlation as well as spectral correlation. In order to show the effectiveness of the proposed method, computer simulations and an experiment are carried out using a six-channel video camera. As a result, it is assured that the proposed method improves color estimation accuracy and suppresses color noise.

An interferometer that uses a cyclic design as double-focus element is described. While preserving most of the merits of a common-path interferometer, this system has no difficulty in applying phase stepping for interferogram analysis.

Here, we propose a new method to enhance the sensitivity of the reflectance spectrum to the scattering feature of the superficial tissue layer. This method is based on multiple discriminant analysis (MDA) in the eigen subspace of the spectrum. Considering the application of scattering imaging, we evaluated this method by performing multispectral imaging of two-layered tissue phantoms. A color map converted from the spectral reflectance well corresponds to variations in the size of the scatter in the first layer. In order to confirm our proposed method works well under more realistic conditions, we performed the computational simulations of the light propagation in the tissue. We used the simulation model combined with the Monte Carlo and the Mie scattering. Its conditions like the slab geometry and the particle distribution of the cell nucleus were estimated by the image measuring of pathological slices. Results on simulations show the possibility of enhancing the sensitivity of the reflectance spectrum to the scattering feature of the superficial tissue layer.

We propose a new method for enhancing the sensitivity of the reflectance spectrum to the scattering feature of the superficial tissue layer. This method is based on multiple-discriminant analysis in the eigensubspace of the spectrum. Considering the application of scattering imaging, we evaluated this method by performing multispectral imaging of two-layered tissue phantoms. A color map converted from the spectral reflectance corresponds well to variations in the size of the scattering in the first layer.

Multispectral imaging is receiving attention in medical color imaging, as high-fidelity color information can be acquired by the multispectral image capturing. On the other hand, as color enhancement in medical color image is effective for distinguishing lesion from normal part, we apply a new technique for color enhancement using multispectral image to enhance the features contained in a certain spectral band, without changing the average color distribution of original image. In this method, to keep the average color distribution, KL transform is applied to spectral data, and only high-order KL coefficients are amplified in the enhancement. Multispectral images of human skin of bruised arm are captured by 16-band multispectral camera, and the proposed color enhancement is applied. The resultant images are compared with the color images reproduced assuming CIE D65 illuminant (obtained by natural color reproduction technique). As a result, the proposed technique successfully visualizes unclear bruised lesions, which are almost invisible in natural color images. The proposed technique will provide support tool for the diagnosis in dermatology, visual examination in internal medicine, nursing care for preventing bedsore, and so on.

The scatter in single photon emission computed tomography (SPECT) contains activity information and some reports showed that it is possible to use this information for improving image quantity. The method is modeling scatter in multiple energy windows in reconstruction. However, what the performance and what noise behavior will be when using scattered radiation in reconstruction are the problems remaining unanswered. Here, the authors investigate the method of modeling scatter in multiple energy windows in the cases of few projection views. The system performance is analyzed by using singular value decomposition (SVD). For investigating noise behavior, the reconstruction is accomplished by estimating the variance of reconstructed voxel values. The effectiveness of using scatter in noise cases is evaluated by resolution kernel analysis. The results show that the improvements due to using scatter are shown in normalized mean square error (NMEM) of reconstructed images and the resolution kernels. When photon counts fall below about one million, there is still some effectiveness of using scatter in the cases of few projection views.

In pathological diagnosis, a tissue sample is stained and observed under a microscope. But the color of the reproduced image varies due to the stain conditions and the characteristics of observation devices. This paper proposes a method for quantification of stain conditions from microscopic image taken by a multispectral digital camera. In the proposed method, the transmittance spectra are estimated from the multispectral image, and the amount of stain color pigments is obtained based on the Beer-Lambert law. Through the experiment using the Hematoxylin & Eosin stained tissue samples, it is confirmed that the concentration of both Hematoxylin and Eosin pigments are successfully estimated by the proposed method.

We have applied projection X-ray microscope for three- dimensional (3D) structure analysis by means of cone-beam computed tomography. The projection images of small insect, Omiscus Porcellio, were recorded in every 1 degree for whole direction (360 degree) with a stepping motor controlled sample rotator. The images were recorded with cooled CCD camera (HAMAMATSU C4880) which detect X-ray directly. The 3D image was reconstructed from cone-beam projections using back-projection algorithm. The resolution of the reconstructed 3D image (256 x 256 x 256 pixels) was about 20 micrometers . The digestive organs were clearly visualized in 3D.

A method to reproduce images on an object under various observation geometries is presented. In this method, a multispectral image sequence is captured with rotating the object under a point light source, where spectral distribution and the position are measured. The diffuse and specular reflection images are decomposed from the captured images based on the dichromatic reflection and the Lambertian models. The angular distribution of reflected light is obtained by the decomposed images, and the images under new observation geometry are synthesized by using light-ray rearrangement technique. In the experiments using two types of 2D objects, leather and fabric, it is confirmed that synthesized images under new illumination geometry are almost the same as the images actually captured under the new geometry.

We have developed a projection X-ray microscope by modifying a scanning electron microscope (SEM), thus simplifying optical alignment and focusing process. When the object was much larger than the resolution of this microscope (0.1 μm), the edge of the image was enhanced due to Fresnel diffraction of partially coherent light. Thus the projection images such as thin filaments in biological objects showed enough contrast even their absorption contrast was very low. Because there are no optical elements for X-ray (e.g. zone plate), this microscope has long focal depth. This means we can obtain the projection image of thick sample at one time without preparing thin sections of the sample. Taking this advantage we have applied this microscope for three-dimensional structure analysis by means of computed tomography.

In order to reproduce the natural color of object on color display devices, such as CRT and LCD (liquid crystal display), the saturation of the reproduced color is limited by the gamut of the display device. This paper presents a method to increase the color gamut by using more than three primary colors generated by a holographic optical element (HOE). The light diffracted by HOE is used to generate multiprimary colors, and the color image with extended color gamut is displayed by LCD device. Both transmission- and reflection-type systems suitable for projection displays are proposed, and the capability of increasing the gamut is discussed. The experimental result using transmission-type HOE is also demonstrated.

In order to give medical doctors objective information of the internal surface of the organs, which will lead to an improvement of the quality of the endoscopic diagnosis, it is necessary to develop a method to quantitatively measure colors from the digital images of CCD endoscope. However, when the internal surface of the human digestive organs is illuminated by the light of the endoscope, images captured by the endoscope become reddish compared to the original object due to the reflections by the surrounding red mucosal surface. This phenomenon makes it difficult to measure the object color correctly. We propose a method to compensate the color shift of illumination and to estimate the color of the mucous internal surface from CCD endoscopic images. In this method, the spectral reflectance of the internal surface and the spectral distribution of the illumination are represented by a weighted sum of some functions given by the statistical analysis of the surface reflectances. Each weighting factor is estimated from sequential images captured by the CCD endoscope. The effectiveness of the proposed method is confirmed by a basic experiment using a CCD endoscope and color charts.

SPECT imaging system has shift-variant characteristics due to nonuniform attenuation of gamma-ray, collimator design, scattered photons, etc. In order to provide quantitatively accurate SPECT images, these shift-variant characteristics should be compensated in reconstruction. This paper presents a method to correct the shift-variant characteristics based on a continuous-discrete mapping model. In the proposed method, the projection data are modified using sensitivity functions so that filtered backprojection (FBP) method can be applied. Since the projection data are assumed to be acquired by narrow ray sum beams in the FBP method, narrow ray sum beams are approximated by a weighted sum of sensitivity functions of the measurement system, then the actual projection data are corrected by the weighting factors. Finally, FBP method is applied to the corrected projection data and a SPECT image is reconstructed. Since the proposed method requires the inversion of smaller matrices than the conventional algebraic methods, the amounts of calculation and memory space become smaller, and the stability of the calculation is greatly improved as well. The results of the numerical simulations are also demonstrated.

We developed a double-axis fluorescence microscope as a new type of 3D microscope, in which two conventional microscopes are placed perpendicularly to one another. This optical microscope provides a solution to extend the spatial frequency band in the depth direction, which is greatly limited for conventional single-axis microscopes. In addition, this equipment has a capability of implementing a fast image acquisition system by simultaneously taking images through both microscopes. We evaluated the 3D imaging properties of our system using 3D observation images of a micro-fluorescent sphere. In order to reconstruct 3D images of micro-objects, we applied a CT-based method we proposed to the 3D microscopic imaging system. Our experiments using a biological micro-specimen verified usefulness and effectiveness of our system.