GSURE criterion for unsupervised regularized reconstruction in tomographic diffractive microscopy.

We propose an unsupervised regularized inversion method for reconstruction of the 3D refractive index map of a sample in tomographic diffractive microscopy. It is based on the minimization of the generalized Stein's unbiased risk estimator (GSURE) to automatically estimate optimal values for the hyperparameters of one or several regularization terms (sparsity, edge-preserving smoothness, total variation). We evaluate the performance of our approach on simulated and experimental limited-view data. Our results show that GSURE is an efficient criterion to find suitable regularization weights, which is a critical task, particularly in the context of reducing the amount of required data to allow faster yet efficient acquisitions and reconstructions.

High numerical aperture holographic microscopy reconstruction with extended z range.

A holographic microscopy reconstruction method compatible with a high numerical aperture microscope objective (MO) up to NA=1.4 is proposed. After off-axis and reference field curvature corrections, and after selection of the +1 grating order holographic image, a phase mask that transforms the optical elements of the holographic setup into an afocal device is applied in the camera plane. The reconstruction is then made by the angular spectrum method. The field is first propagated in the image half-space from the camera to the afocal image of the MO optimal plane (the plane for which the MO has been designed) by using a quadratic kernel. The field is then propagated from the MO optimal plane to the object with the exact kernel. Calibration of the reconstruction is made by imaging a calibrated object such as a USAF resolution target for different positions along z. Once the calibration is done, the reconstruction can be made with an object located in any plane z. The reconstruction method has been validated experimentally with a USAF target imaged with a NA=1.4 microscope objective. Near-optimal resolution is obtained over an extended range (±50 µm) of z locations.

Vibration of low amplitude imaged in amplitude and phase by sideband versus carrier correlation digital holography.

Sideband holography can be used to get field images (E0 and E1) of a vibrating object for both the carrier (E0) and the sideband (E1) frequency with respect to vibration. Here we propose to record E0 and E1 sequentially and to image the product E1E0* or the correlation 〈E1E0*〉. We show that these quantities are insensitive to the phase related to the object roughness and directly reflect the phase of the mechanical motion. The signal to noise can be improved by averaging E1E0* over a neighbor pixel, yielding 〈E1E0*〉. Experimental validation is made with a vibrating cube of wood and a clarinet reed. At 2 kHz, vibrations of amplitude down to 0.01 nm are detected.

Noise and signal scaling factors in digital holography in weak illumination: relationship with shot noise.

We have performed off-axis heterodyne holography with very weak illumination by recording holograms of the object with and without object illumination in the same acquisition run. We have experimentally studied how the reconstructed image signal (with illumination) and noise background (without) scale with the holographic acquisition and reconstruction parameters that are the number of frames and the number of pixels of the reconstruction spatial filter. The first parameter is related to the frequency bandwidth of detection in time, the second one to the bandwidth in space. The signal to background ratio varies roughly like the inverse of the bandwidth in time and space. We have also compared the noise background with the theoretical shot-noise background calculated by Monte Carlo simulation. The experimental and Monte Carlo noise background agree very well with each other.