Computational Optical Microscopy

Phase Shifting & White Light Interferometry

Inteferometric techniques, based on wave interference phenomenon, are being widely used in astronomy, surface metrology, geodesy, and seismology, among other areas. In optical metrology, they allow for high-resolution surface profiling, with sub-nanometer accuracy. Most industrial interferometers work by splitting the amplitude of an incident coherent wave into 2 separate beams which are then directed onto the analyzed sample and a reference mirror. The reflected beams are recombined and the fringe pattern, resulting because of the optical path difference traveled by the two beams after the splitting, is analyzed.

In Phase Shifting Interferometry (PSI) the bandwidth of the incident wave is small (a few nanometers or less) and the reference mirror is translated in equal steps while the resulting interferograms are recorded on a digital camera. The phase difference between adjacent pixels is calculated and converted to height differences. The vertical resolution is excellent, but the height difference between adjacent pixels that can be unambiguously determined is limited.

In White Light Interferometry (WLI) the bandwidth of the incident wave is considerably larger which leads to a noticeable reduction in the spatial coherence of the beam. The mirror is also translated in equal steps and the interference signal recorded. The maximum of the envelope of the interference signal is obtained when the optical path difference between the beam is zero. The vertical resolution is lower than in the case of PSI, but samples with arbitrary vertical profiles can be unambiguously measured.

Digital Holography

Digital holography, based on numerical wave-front reconstruction from digitally recorded holograms, is a powerful imaging method with important applications in biology, medicine, and metrology.  Compared with traditional microscopy, which only records information about the investigated object’s wave-front intensity, digital holography also records information about its phase which later can be used to determine depth or thickness information. The holographic process is based on the interference between a reference beam and the light coming from the sample when illuminated with a long-range coherent beam. The usual reconstruction process is based on Fresnel approximation,  valid when the hologram’s dimensions are considerably smaller than the distance to the hologram plane.

An important limitation of the single wavelength digital holography is the phase unwrapping ambiguity, which imposes a limitation in the maximum height difference between adjacent pixels. To overcome this, phase imaging digital holography using two or more wavelengths can be used.

Optical Coherence Tomography

Optical Coherence Tomography (OCT) is a low-coherence interferometry technique used in medical imaging for 3D profiling of transparent and semi-transparent organs. The light scattered by regions of higher density in the biological tissue will interfere with the reference beam and create a detectable interference pattern when the optical path difference (OPD) between the beams is negligible. However, interferometric signal is observed only over a limited depth of sample because of the low coherence of the light source. Therefore, lateral scanning records one thin optical slice of the sample at a time. Finally, an entire three-dimensional image of the tissue can be reconstructed by performing multiple lateral scans and moving the reference mirror between each scan.

Two main approaches to OCT are frequently used. In the time domain optical coherence tomography (TD-OCT) the reference mirror is scanned axially, thus modifying the optical path difference between the reference and sample beams. The maximum envelope of the interference pattern identifies the location of the zero OPD and, thus, the position of the higher density tissue region. In the Fourier domain optical coherence tomography (FD-OCD), the position of the reference mirror is fixed, but the broadband interference signal is spectrally resolved, usually by a dispersive element inserted in from of the CCD camera. Thus, the imaging speed is increased at the expense of reducing the available signal at each pixel in the detector. The frequency of the interference fringes as a function of source wavelength identifies the position of the higher density tissue region in the sample.

Confocal Microscopy

Confocal Microscopy technique is used extensively in Biology and Semiconductor Industry because of its increased resolution and contrast capabilities. These are achieved by two main modifications of the standard microscopy setup: point-wise illumination and a spatial pinhole placed at the confocal plane of the lens which eliminates the out-of-focus light. In order to build an image using the confocal principle, the focused spot of light must be scanned across the specimen, hence the development of confocal laser scanning microscopy (CLSM). Increased vertical resolution is also obtained in confocal setup and the 3D profilig of the specimen is  performed by combined lateral and axial scanning.

Besides the optical sectioning capability, CLSM offers the advange of adjustable lateral resolution, as this depends directly on the size of the pinhole. If the pinhole size  is larger than the central feature of the diffraction pattern, called the “Airy disk”, then  the resolution is approximatively equal to the diffraction-limited resolution in an  ordinary microscope. Upon closing the pinhole to diameters below that of the Airy disk, the lateral  resolution increases – corresponding to a smaller FWHM of detectable features.  The limit is reached for the theoretical case of a completely closed pinhole, where  the theory predicts an improvement of some 30%. Additional lateral resolution can be achieved by deconvolving the microscope objective response function from the measured signal, a procedure usually termed super-resolution or image reconstruction.

With the advent of increased computational power, an alternative to confocal microscopy  is offered by the numerical deconvolution of standard microscopy images performed by computer-based algorithms that  calculate and remove out-of-focus information from fluorescence images.