A four-dimensional impulse response function for the digital holographic three-dimensional imaging spectrometry has been fully derived in closed form. Due to its factorizing nature of the mathematical expression of four-dimensional impulse response function, three-dimensional spatial part of impulse response function directly corresponds to threedimensional point spread function of in-line digital holography with rectangular aperture. Based on these mathematical results, this paper focuses on the investigation of spectral resolution and three-dimensional spatial resolution in digital holographic three-dimensional imaging spectrometry and digital holography. We found that the theoretical prediction agree well with the experimental results. This work suggests a new criterion and estimate method regarding threedimensional spatial resolution of in-line digital holography.
We present a method to obtain a set of spectral component of three-dimensional images based on measurements of hyperbolic volume interferogram. The method uses an improved two-wavefront folding interferometer incorporating with a single detector of high sensitivity. The method may apply to usual polychromatic objects because it is kind of incoherent holography combined with Fourier transform spectroscopy. First experimental result of the method is shown to demonstrate the capability to acquire continues spectral profile of three-dimensional polychromatic object.
This paper presents a new method of digital holographic three-dimensional imaging spectrometry. The method is based on the measurement of new type of volume interferogram, called Rotated-Hyperbolic-type volume interferogram, obtained with the existing interferometer. We report the first demonstration of the method in which a monochromatic point source is used as the measured object. The results include 3-D spatial information and spectral information of a monochromatic point source. This experimental result corresponds to the impulse response function defined over a four dimensional (x, y, z, k) space. As a result, the method is confirmed to have the superior imaging characteristics in the z direction.