A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a
number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution
complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and
digitally extend a microscope’s depth of focus beyond the physical limitations of its optics. As a demonstration, we built a
microscope prototype with a resolution of 0.78 µm, a field of view of ∼120 mm^2 and a resolution-invariant depth of focus
of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The
reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one
that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

Wide-field, high-resolution Fourier ptychographic microscopy

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process We demonstrate two applications of the reported scheme In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object We also demonstrate a reconstruction resolution better than the detector pixel limit (ie, pixel super-resolution) In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field This platform’s maximum achievable resolution is ultimately determined by the camera’s traveling range, not the aperture size of the lens The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy

Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging

We utilize synthetic-aperture Fourier holographic microscopy to resolve micrometer-scale microstructure over millimeter-scale fields of view. Multiple holograms are recorded, each registering a different, limited region of the sample object's Fourier spectrum. They are "stitched together" to generate the synthetic aperture. A low-numerical-aperture (NA) objective lens provides the wide field of view, and the additional advantages of a long working distance, no immersion fluids, and an inexpensive, simple optical system. Following the first theoretical treatment of the technique, we present images of a microchip target derived from an annular synthetic aperture (NA = 0.61) whose area is 15 times that due to a single hologram (NA = 0.13); they exhibit a corresponding qualitative improvement. We demonstrate that a high-quality reconstruction may be obtained from a limited sub-region of Fourier space, if the object's structural information is concentrated there.

High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy

Fourier ptychography (FP) is a recently developed imaging approach that bypasses the resolution limit defined by the lens’ aperture. In current FP imaging platforms, systematic noise sources come from the intensity fluctuation of multiple LED elements and the pupil aberrations of the employed optics. These system uncertainties can significantly degrade the reconstruction quality and limit the achievable resolution, imposing a restriction on the effectiveness of the FP approach. In this paper, we report an optimization procedure that performs adaptive system correction for Fourier ptychographic imaging. Similar to the techniques used in phase retrieval, the reported procedure involves the evaluation of an image-quality metric at each iteration step, followed by the estimation of an improved system correction. This optimization process is repeated until the image-quality metric is maximized. As a demonstration, we used this process to correct for illumination intensity fluctuation, to compensate for pupil aberration of the optics, and to recover several unknown system parameters. The reported adaptive correction scheme may improve the robustness of Fourier ptychographic imaging by factoring out system imperfections and uncertainties.

Adaptive system correction for robust Fourier ptychographic imaging

Theoretical analysis shows that, to improve the resolution and the range of the field of view of the reconstructed image in digital lensless Fourier transform holography, an effective solution is to increase the area and the pixel number of the recorded digital hologram. A new approach based on the synthetic aperture technique and use of linear CCD scanning is presented to obtain digital holographic images with high resolution and a wide field of view. By using a synthetic aperture technique and linear CCD scanning, we obtained digital lensless Fourier transform holograms with a large area of 3.5 cm×3.5 cm (5000×5000 pixels). The numerical reconstruction of a 4 mm object at a distance of 14 cm by use of a Rayleigh-Sommerfeld integral shows that a theoretically minimum resolvable distance of 2.57 μm can be achieved at a wavelength of 632.8 nm. The experimental results are consistent with the theoretical analysis.

High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning

A new carrier removal method for interferogram analysis using the Fourier transform is presented. The proposed method can be used to suppress the carrier removal error as well as the spectral leakage error. First, the carrier frequencies are estimated with the spectral centroid of the up sidelobe of the apodized interferogram, and then the up sidelobe can be shifted to the origin in the frequency domain by multiplying the original interferogram by a constructed plane reference wave. The influence of the carrier frequencies without an integer multiple of the frequency interval and the window function for apodization of the interferogram can be avoided in our work. The simulation and experimental results show that this method is effective for phase measurement with a high accuracy from a single interferogram.

Suppressing carrier removal error in the Fourier transform method for interferogram analysis

To suppress the aperture diffraction and spectral leakage effects in the reconstruction process of the digital hologram and to maintain the original information recorded in the hologram, a novel reconstruction method based on extension and apodization of the digital hologram is presented, by which the original hologram can be extended by filling the average intensity values of the boundary, and the extended hologram is apodized by use of the constructed window function. As a sample, the digital hologram of the static particle field is recorded and numerically extended and then apodized with the appointed window. Finally, an unabridged and clear digital holographic image is reconstructed from the extended and apodized hologram. The experimental results confirm that this method cannot only eliminate the black-and-white diffraction fringes in the reconstructed image, but also attain the unabridged image with high quality.

Improving the reconstruction quality with extension and apodization of the digital hologram.

The invention discloses a method for analyzing digital interference fringe and a device for detecting optical component surface shape. The main technical characteristic of the invention is that firstly a digital interference fringe image times a window function to expand the width of main lobe of interference fringe image spectrum and to inhibit side lobe of the interference fringe image spectrum; carrying out Fourier analysis on the digital interference fringe image; estimating space carrier frequency of the digital interference fringe by adopting an algorithmic method of a barycentric coordinates of a barycentric group; and the method is also used for the frequency shift of the digital interference fringe image, thus effectively inhibiting error to measurement by a hurdle effect. Besides, the device for detecting optical component surface shape constructed based on the method for analyzing digital interference fringe can carry out high-accuracy analysis on the interference fringe ofthe space carrier frequency when frequency sampling interval is not integral multiple, and has simple structure and good measuring instantaneity.

Method for analyzing digital interference fringe and device for detecting optical component surface shape

The invention discloses an aspheric optical element surface shape detection device. Based on prior interference method surface shape detection devices, the aspheric optical element surface shape detection device realizes the measurement of the light intensities of detection light waves and reference light waves by additionally arranging two controllable optical stops and can acquire phase shift interference fringes by additionally arranging piezoelectric ceramics. An aspheric surface shape measurement software package can conveniently acquire a phase offset between the surface shape and an ideal surface shape of an aspheric optical element to be detected by computing the phase offset between the surface shape to be detected and a standard surface shape of the aspheric optical element to bedetected and the phase offset between the ideal surface shape and the standard surface shape of the aspheric optical element to be detected. Therefore, the aspheric optical element surface shape detection device can effectively solve the surface shape detection problem of aspheric optical elements with large offset without a practical processing computed hologram, thereby reducing detection cost,shortening detection cycle and improving detection accuracy.

Qi Fan

Papers

High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning

Suppressing carrier removal error in the Fourier transform method for interferogram analysis

Improving the reconstruction quality with extension and apodization of the digital hologram.

Method for analyzing digital interference fringe and device for detecting optical component surface shape

Aspheric optical element surface shape detection device