A technique to perform two-wavelengths digital holographic microscopy (DHM) measurements with a single hologram acquisition is presented. The vertical measurement range without phase ambiguity is extended to the micron-range, thanks to the resulting synthetic wavelength defined by the beating of two wavelengths with a separation of about 80nm. Real-time dual-wavelength imaging is made possible by using two reference waves having different wavelengths and propagation directions for the hologram recording. The principle of the method is exposed and experimental results concerning a 1.2μm m high test sample as well as a moving micro-mirror are presented. To the extent of our knowledge, this is the first time that real-time synthetic beat-wavelength digital holography measurements are reported.

/pdf/real-time-dual-wavelength-digital-holographic-microscopy-1syba5vfwd.pdf

Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.

Parallel two-step phase-shifting digital holography

We present a detailed analysis of image formation in digital Fresnel holography. The mathematical modeling is developed on the basis of Fourier optics, making possible the understanding of the different influences of each of the physical effects invoked in digital holography. Particularly, it is demonstrated that spatial resolution in the reconstructed plane can be written as a convolution product of functions that describe these influences. The analysis leads to a thorough investigation of the effect of the width of the sensor, the surface of pixels, the numerical focusing, and the aberrations of the reference wave, as well as to an explicit formulation of the Shannon theorem for digital holography. Experimental illustrations confirm the proposed theoretical analysis.

General theoretical formulation of image formation in digital Fresnel holography

We present state-of-the-art dual-wavelength digital holographic microscopy (DHM) measurement on a calibrated 8.9 nm high chromium thin step sample and demonstrate sub-nanometer axial accuracy. By using a modified DHM reference calibrated hologram (RCH) reconstruction method, a temporal averaging procedure and a specific dual-wavelength DHM arrangement, it is shown that specimen topography can be measured with an accuracy, defined as the axial standard deviation, reduced to at least 0.9 nm. Indeed for the first time to the best of our knowledge, it is reported that averaging each of the two wavefronts recorded with real-time dual-wavelength DHM can provide up to 30% spatial noise reduction for the given configuration. Moreover, the presented experimental configuration achieves a temporal stability below 0.8 nm, thus paving the way to Angstrom range for dual-wavelength DHM.

/pdf/axial-sub-nanometer-accuracy-in-digital-holographic-58f01c60rj.pdf

Axial sub-nanometer accuracy in digital holographic microscopy

Recent developments in interferometry for microsystems metrology

An endoscope is used in pulsed digital holography to simultaneously evaluate in-plane and out- of-plane transient and harmonic displacements on a flat metallic plate. The plate is illuminated from two different directions. The optical path for each illumination direction is matched to its corresponding reference beam, but also in such a way that each object-reference beam pair optical path is mismatched such that they are incoherent and can be stored in a single CCD frame. As is typical in these types of interferometric arrangement, two digital holograms are needed to compare two different states of the plate. Each hologram is Fourier transformed and due to the incoherence introduced, two separate spectra are readily identified, each belonging to an object-reference beam pair. On comparing by subtraction the phase obtained from the two pulsed digital holograms, it is possible to gather quantitative in-plane and out-of- plane results from transient and harmonic displacements.

Tonatiuh Saucedo A

Papers

Simultaneous two-dimensional endoscopic pulsed digital holography for evaluation of dynamic displacements.