The operation of the Digital Holographic/Speckle Interferometer (DHSI) is based on the double-exposure holographic interferometry, when two or more holographic images of a tested object that correspond to different phases of a surface deformation process are registered with the laser light by the digital video camera.
To register a digital hologram, a laser beam is divided into a scene beam, which illuminates the object, and a reference beam, which is sent directly to the receiving sensor of the digital video camera. The scene beam illuminates the object in the direction ki. A portion of light reflected in the direction kv (the observation direction) goes through an optical focusing system and forms the object’s image at the receiving sensor of the digital video camera. The hologram of the focused image forms on the CCD matrix of the digital camera as a result of the interference between the reference beam and the scene beam.
Let R(x, y) be a smooth reference wave, and U(x, y) be a scene wave coming from the object. Then intensity registered at the CCD matrix of the receiving video camera is described with the expression:
|IH (x, y) = |RH (x, y)|2 + |UH(x, y)|2 + RH (x, y) U*H (x, y) + R*H (x, y) UH(x, y)||(1),|
where index H marks the hologram plane, and an asterisk * means a complex conjugation. Intensity described by formula (1) is registered with a two-dimensional electronic device consisting of M x N sensitive cells (pixels) with dimensions Dx x Dy, and therefore can be written as a functionIH(mDx, nDy), where m and n are integers. The last two terms of formula (1) contain information about amplitude and a phase of the wave. This information can be derived with the spatial filtering based on the Fourier transform of the registered array, which allows to extract and to filter one of those two terms. Both those terms are separated in the Fourier plane as a result of a slight tilt of the reference beam in respect to the scene beam. After filtration and the Fourier inversion, the complex amplitude of the scene wavefront can be obtained. Knowing a resulting digitized complex amplitude UH(mDx, nDy) , a phase of the wavefront of the scene wave can be calculated:
where Re and Im mean a real and imaginary parts of the complex number respectively.
Subtracting values of phases of the scene field calculated for two object states (for instance, before and after loading) gives a value of the phase difference, which allows to calculate displacement of spots of the object d as a result of loading in the direction s by the formula:
where l is a laser beam wavelength, s is an interferometer sensitivity vector determined by the formula:s = ki – kv, and ki and kv are unit vectors of illumination and observation respectively.
To measure a full vector of displacement, a scheme with three different sensitivity vectors is used, which allows to receive three linear-independent equations of the form (3) and to calculate projections of the full vectors of the axis of coordinates.
Latest achievements in the area of laser physics, computer and digital technologies used in development of the DHSI family, made it possible to drastically increase the sensitivity, efficiency and noise immunity of the method as compared to the classic holography.
The DHSI Use Scheme
To conduct measurements, the DHSI should be directed on the object, and the computer monitor will display the object’s image. After that, depending on the task, a particular loading method should be used and a series of digital holograms registered. Finally, results should be processed using special software.
The Nanotouch DHSI family allows to realize ALL main methods of holographic measurements.