Optical path difference

Let us consider investigation of stresses in a 3-D specimen. It has been shown [1] that in the case of weak birefringence a 3-D specimen can be investigated in a conventional transmission polariscope as if it were a two dimensional specimen. On every ray of light it is possible to determine the parameter of the isoclinic and the optical path difference A. The latter are related to the components of the stress tensor on the ray by linear integral relationships... 

To efficiendy drive the development of improved substrate materials, the limiting values of birefringence have to be known this is especially tme for WORM and EOD(MOR) substrate disks. These limit values were laid down by the ANSI (American National Standard Institute) Technical Standard Committee (186—188). For 5.25 in. WORM disks, the ANSI document X 3 B 11/88-144 recommends a maximum LEP value of 9% this corresponds to an optical path difference perpendicular to the plane of the disk of not more than 80 nm/mm (double path). For 5.25 in. EOD(MOR) disks, more stringent conditions apply (ANSI-document X 3 B 11/88-049), which also allow calculation of the allowed range. 

In an industrial-design FTIR spectrometer, a modified form of the G enzel interferometer is utilized.A geometric displacement of the moving mirrors by one unit produces four units of optical path difference (compared with two units of optical difference for a Michelson type interferometer). The modified Genzel design reduces the time required to scan a spectrum and further reduces the noise effects asstxiated with the longer mirror translation of most interferometers. 

In order to compensate for the distortions in the wavefront due to the atmosphere we must introduce a phase correction device into the optical beam. These phase correction devices operate by producing an optical path difference in the beam by varying either the refractive index of the phase corrector (refractive devices) or by introducing a variable geometrical path difference (reflective devices, i.e. deformable mirrors). Almost all AO systems use deformable mirrors, although there has been considerable research about liquid crystal devices in which the refractive index is electrically controlled. 

Figure 19. The optical path difference A/ as a function of the x-coordinate with the interferogram shown below. The shear b is taken to be 0.07 cm and D x f to be 2 x 10" cm (Reprinted from Ref 101 with permission from Z. Natulforschung.)...

Such measurement provides the magnitude of birefringence, but not its sign. In addition, identical transmission values will be observed for multiple birefringence orders, that is, whenever the optical path difference, dAn, becomes a multiple of X. The main interest of this method arises from its excellent time resolution, below 1 ms, that is readily achieved using a low-power (e.g., 5 mW) continuous-wave laser and a photodiode. If the sample is initially isotropic, it is possible to follow the birefringence order to obtain quantitative results. For improved accuracy, a second (reference) photodiode or a beam chopper and a lock-in amplifier can be used. 

This interferometric dilatometer consists of a rather simple and small Michelson interferometer, in which the two arms are parallel, and of a 4He cryostat, in which the sample to be measured is hold. The sample is cooled to 4 K, and data are taken during the warm up of the cryostat. The optical path difference between the two arms depends on the sample length hence a variation of the sample length determines an interference signal. The Michelson interferometer consists of a He-Ne stabilized laser (A = 0.6328 xm), two cube corner prisms, a beam splitter, three mirrors and a silicon photodiode detector placed in the focal plane of a 25 mm focal length biconvex lens (see Fig. 13.1). 

The total optical path difference between the two arms of the interferometer, for a sample length of about 50 mm, is of the order of 10 mm or less, minimizing the systematic error due to laser frequency fluctuations. To reduce the thermal effects on the interferometer assembly, the interferometer support plate is stabilized to a temperature slightly higher than room temperature and insulated from air currents by a polystyrene foam shield. The temperature variation of the interferometer support is kept below 0.1 K. 

The discussion in the present section concerns only dispersive optical spectroscopy. We shall not treat the resolution characteristic of a Fourier interferometric spectrometer, which is determined by the optical path difference scanned and the apodizing function used. Nevertheless, these... 

However, it is to be noted that the Fourier transform integrals have infinite limits while the optical path differences are finite so modifications or approximations must be made. We will use the approximation of the limits between —L and + L where L is the maximum distance of the mirror drive. So... 

The signal seen at the detector for a given value of the optical path difference (OPD), given by the symbol 6, is dependent upon the wavelengths, amplitudes, and phases of the components of the radiation. Constructive interference for all components occurs only at S = 0, where the maximum signal is observed (often referred to as the centerburst or central maximum). The signal that is seen at the detector as a function of S, 1(5) for an ideal interferometer, is given by... 

The optical path difference over which the interferogram can be digitized is limited by the dimensions of the interferometer. 

Time-resolved chemiluminescence spectra are obtained as follows. For a given optical path difference, the entire temporal profile of the pulse of product IR chemiluminescence is recorded at the detector, amplified, digitized (up to 10 ns resolution) and stored directly on hard disc for a preset number of photolysis laser shots, the number depending on the SNR of the system. The C02 laser energy for each shot is recorded by a pyroelectric... 

Figure 3. The overall temporal profile of the infrared emission as seen by the detector at four positions of optical path difference 5, in the vicinity of the position of zero optical difference <5 = 0. The data shown are for emission from highly vibrationally excited C02, taken with a temporal resolution of 3 ns and with one shot of the C02 laser per mirror position, and illustrate how both the intensities and the time profiles of the emission, arising from the production and decay of many vibrational levels, change as a function of 5. Reproduced with permission from Ref. 37.

In its basic design, the equipment is similar to a 2-D TL glow-curve system as described previously, but with the addition of a modified Twyman-Green, Michelson type, interferometer between the oven and the photomultiplier. As the sample is heated, the TL signal is recorded while the movable mirror of the interferometer is scanning a given optical path difference in a preset number of steps. The interference pattern corresponding to each one-way scan... 

Although several techniques are available for the determination of refractive index, only the double embedding procedure has been used with wood specimens (Boutelje 1972, Donaldson 1985a). This procedure involves measuring optical path difference (o.p.d.) successively in two different reference media. Selection of reference media depends on a number of criteria ... 

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