Luis Martı́-López

Validity conditions for the radiative transfer equation.

We compare the radiative transfer equation for media with constant refractive index with the radiative transfer equation for media with spatially varying refractive indices [J. Opt. A Pure App. Opt. 1, L1 (1999)] and obtain approximate conditions under which the former equation is accurate for modeling light propagation in scattering media with spatially varying refractive indices. These conditions impose restrictions on the variations of the refractive index, the gradient of the refractive index, the divergence of the rays, the frequency of modulation, and the widths of light pulses, which are related to the mean refractive index, the absorption coefficient, and the reduced scattering coefficient of the medium. Each condition is geometrically interpreted. Some implications of the results are discussed.

Incoherent superposition of off-axis polychromatic Hermite–Gaussian modes

We study a statistical ensemble of multimode laser beams. Each beam is made up of an incoherent superposition of off-axis polychromatic Hermite-Gaussian modes. We obtain analytic expressions for the squared beam radius, the waist position, the Rayleigh range, the skewness parameter, the kurtosis parameter, and the squared beam-propagation factor. We demonstrate that the squared beam radius has a quadratic dependence on the distance from the waist plane. The skewness parameter may be different from zero in the near-field zone, but it tends to zero in the far-field zone. The kurtosis parameter in the far-field zone coincides with the kurtosis parameter of the incoherent superposition of on-axis modes.

Propagation of polychromatic Gaussian beams through thin lenses.

The transformation by a lens of a polychromatic laser beam composed of on-axis superposed monochromatic TEM00 Gaussian modes in the paraxial approximation is studied. The chromatic aberrations are described by allowing the waist position on the z axis and the Rayleigh range to depend on wavelength. The beam radius, the far-field divergence, the Rayleigh range, the beam product, the beam propagation factor, and the kurtosis parameter are calculated. The relationship between the fourth-order and the second-order moments of Hermite-Gaussian and Laguerre-Gaussian modes is obtained and is used for calculating kurtosis parameter. The results are generalized to polychromatic modes of higher orders. It is shown that the on-axis superposition of monochromatic TEM00 modes with no chromatic aberration is leptokurtic.

Effect of chromatic aberration on Gaussian beams: non-dispersive laser resonators

Abstract The propagation of a non-monochromatic (polychromatic) TEM 00 Gaussian beam in vacuum, its passage through a thin plate and its transformation by a thin lens are studied in the case of a non-dispersive laser resonator. The basic assumptions of the model are as follows: optical fields are stationary and plane-polarized, the paraxial wave equation is valid, an equivalent non-dispersive hemiconfocal resonator represents the lasing medium and its stable resonator, the laser emits in a single mode. It is also assumed that the plate and the lens have large transverse dimensions. Mathematical expressions, for beam radius, divergence, radius of curvature and beam parameter product, are obtained. A beam quality factor for polychromatic Gaussian beams is defined and its value calculated in each case of interest. It is proposed to simulate a dispersive laser resonator by a non-dispersive resonator complemented with a plate and/or a thin lens.

Out-of-plane displacement measurement by means of endoscopic moiré interferometry

An endoscopic moire technique is proposed for measuring out-of-plane displacements in difficult to reach places. The Ronchi grid is projected onto the tilted object with one endoscope with a 0° viewing angle. The object with the projected grid is imaged by a second endoscope with a 30° viewing angle onto a charge-coupled device. The captured images are stored in a PC, and are used to calculate the out-of-plane displacement of the object with a phase stepping technique. A computer generated grating method is used instead of a physical phase-shift device in the optical setup. This allows designing a set of three reference grids with profiles closely similar to the projected grating. The technique is robust against problems associated with the temporal shifting method, such as nonlinear phase shift and noise. To test the feasibility of the technique the measurement of out-of-plane displacements of about 35 μm of a latex membrane under deformation is demonstrated. The advantages and disadvantages are discussed.

Effect of primary aberrations on transverse displacement of laser speckle patterns

The effect of primary aberrations on the transverse displacement of laser speckle patterns in the real image plane due to transverse displacement of an object is studied in the approximation of Fourier optics. Primary aberrations cause: (i) a complementary displacement of the speckle pattern; and (ii) its decorrelation. The main features of complementary displacements are as follows: (a) the overall complementary displacement is the sum of complementary displacements caused by each one of the primary aberrations; (b) the complementary displacement caused by the spherical aberration is uniform in the image plane; (c) spherical aberration and curvature of field cause complementary displacements that are parallel to the objects displacement; (d) the complementary displacement caused by distortion is always zero on the optical axis; (e) the complementary displacement caused by distortion is free of decorrelation; (f) complementary displacements are non-proportional to the objects displacement; and (g) complementary displacements depend on the position of the illuminating source with the exception of the complementary displacement caused by distortion.

Polychromatic Gaussian beams emitted by dispersive laser resonators

In-vacuum propagation of a polychromatic Gaussian beam emitted by a dispersive laser resonator and its passage through thin plates are studied under following assumptions: optical fields are stationary and plane-polarized, the paraxial wave equation is valid for each monochromatic component of the beam, the waist position and the Rayleigh range depend on wavelength and diffraction edge effects are negligible. Mathematical expressions for beam radius, divergence, beam parameter product and beam propagation factor are obtained. The use of thin plates for waist position achromatization is analyzed.

Applications of speckle interferometry to civil engineering in Cuba

Speckle interferometry has been introduced in Civil Engineering at CUJAE in 1988 as a useful technique in research work. This paper describes some applications of speckle interferometry in civil engineering. Speckle photography has been utilized to study deformation in shearwalls, and also studding of behavior building model under concentrate loading. Displacements were numerically calculated using a finite element method. Electronic Speckle Pattern Interferometry (ESPI) has been used for the measurement of the Youngs modulus in mortars and concrete. Obtained values of the Youngs modulus are in good agreement with reported for mortars or measured by a static compressive technique for concrete.

Effect of compensation for spherical aberration on the transverse displacement of laser speckle patterns

When a rough surface illuminated by coherent light is displaced perpendicularly to the optical axis of an imaging optical system the speckle pattern in the conjugate plane is transversally displaced too. This displacement has two components. The first one is proportional to the object displacement, and the second one depends on wave-front aberrations and, consequently, is strongly related to the optical system that is used. Usually, well-corrected photographic objectives are used for the measurement of transverse displacements by double-exposure laser speckle photography. Since in well-corrected objectives aberrations tend to compensate one another, it seems that the complementary displacement of the speckle pattern, caused by aberrations, is near zero and does not affect the accuracy of the measurement. Here it is analytically shown that the compensation of spherical aberrations does not guarantee a negligible complementary displacement. From the results obtained it follows that well-corrected objectives for laser speckle photography can be regarded as a particular class of photographic objectives, since they not only yield high-quality images but also minimize complementary displacement.

Analysis of the imaging method for assessment of the smile of laser diode bars

We study imaging systems designed to assess the smile of laser diode bars (LDBs). The magnification matrix is derived from the required sampling period and the geometries of the LDBs and the charge-coupled device (CCD) array. These image-forming systems present in-plane pure translation invariance, but in the case of anamorphic ones, lack in-plane rotation invariance. It is shown that the smile parameters of the image of the LDB are linked with the smile parameters of the LDB by simple mathematical expressions. The spatial resolution of such optical systems is estimated at approximately 1 microm for a mean wavelength of lambda approximately 800 nm. Our results suggest that, with the current state-of-the-art, the formation of imaging methods for LDB smile assessment can be used to assess smile heights > or = 1 microm.