Basic Principles of Operation

The VISAR provides a point measurement of an interface velocity with high temporal resolution [13]. The basis of the velocity interferometer is the Doppler shift. If laser light is reflected off of the surface of the moving target, the reflected light will have an associated Doppler shift:

λ=λ01−u c

, (3.2)

where c is the speed of light, λ0 is the incident laser wavelength, uis the velocity of the moving

surface, and λis the Doppler shifted wavelength. If a Doppler shifted beam with frequency ν1 is

combined with itself at a short time later, which now has frequencyν2, the intensity of light can be

expressed as

I = |Es|2=|A1cos(2πν1t+φ1) +A2cos(2πν2t+φ2)|2

=A21cos2(2πν1t+φ1) +A22cos2(2πν2t+φ2) (3.3)

+A1A2cos[2π(ν1+ν2)t+φ1−φ2] +A1A2cos[2π(ν1−ν2)t+φ1−φ2].

The first three terms oscillate at a frequency on the order of the laser light, 1014_{to 10}15_{Hz, which}

is well out of the response range of oscilloscopes. The last term, however, is proportional to the so-called beat frequency, and is something that can be measured experimentally. Thus, the recorded intensity of the combined Doppler shifted light is representative of differential changes frequency, which can be related to differential changes in velocity, as seen in Equation 3.2. The VISAR, shown in Figure 3.5, is an optical system that forces this interference of the reflected light with itself after a known delay.

As shown in Figure 3.5, the reflected light is first sent into a 30/70 beam splitter where 30% of the light is sent directly to a photodetector and the rest is sent into the interferometer. This first photodetector is called the beam intensity monitor, and is used to correct for any changes in the reflected light intensity. The other 70% is sent into a 50/50 beam splitter where half is sent down a free path before being reflected back off of a mirror and combining with light from the second leg, which is sent through an 1/8 wave plate and length of etalon (a high index of refraction glass)

Photo-Detectors Etalon 1/8 wave plate Polarizing B/S B/S Target Beam Intensity Monitor OPL1 OPL2 = OPL1

Figure 3.5: Schematic of VISAR

before being reflected by a mirror. The second leg is arranged such that its optical path length is the same as the first leg. The equivalent path lengths allow for optimal fringe contrast for any reflecting surface, since the divergence of the beams from a diffuse surface will be equal. Thus, the etalon makes it possible to maintain fringe contrast for diffuse surfaces while still providing the necessary time delay in the second leg. This clever arrangement is known as the wide-angle Michelson interferometer [49]. The second key idea of the VISAR is the utilization of Bouricius’ method to produce quadrature phase components [21]. By introducing an effective 1/4 wave plate into the second leg (since the beam passes through the 1/8 wave plate twice), the P component of the laser light is retarded by 90◦, changing the linearly polarized light to circular. When the combined beams are then sent into the polarizing beam splitter, the P and S components of the laser light are separated and then sent into two different photodetectors. The photodetectors, in turn, will record two sets of interferometry fringes that are 90◦out of phase, and are said to be in quadrature. Quadrature is a key feature in this system because it allows for the detection of reversals, that is, acceleration to be distinguished from deceleration [13]. Hemsing’s method of VISAR reduction [47] can be used to produce a continuous fringe count record. This is done by first subtracting out any fluctuations seen in the beam intensity monitor from the measured signals. Since the resulting signal takes the form of a sinusoidal function as shown in Eqn. 3.3, and one signal is exactly 90◦ out of phase with the other, the ratio of the two signals forms a tangent function. Thus, appropriately

unwrapping the tangent gives the fringe count F(t) =tan−1 _s2(t) s1(t) , (3.4) where si= Di(t) Ki −B(t) K0 , (3.5)

and Di(t) is the measured light intensity of the photodetectors (i= 1,2), B(t) is the intensity at the beam intensity monitor, andKi, K0are the appropriate normalization factors. All that remains

is to relate the resulting fringe count,F(t), to the interface velocity. The instantaneous number of fringes can be found be examining the difference in the total number of fringes in each leg, given by dividing the length of the etalon by the wavelength as

N(t)λ(t) =cτ, (3.6)

where τ is the known time delay due to the etalon. Differentiating Equation 3.6 with respect to time results in 4N =−N λ4λ=− cτ λ24λ. (3.7) Using Equation 3.2, 4λ=λ0 1−2u c −λ0= −2u c , (3.8)

where the factor of 2 comes from the fact that the light traverses a round trip in the interferometer so the image velocity detected is actually twice that of the moving object [13,30]. Substituting Eqn. 3.8 into 3.7 gives the velocity in terms of the fringe count:

ut−τ

2

= λ0F(t)

2τ , (3.9)

where4N has been replaced byF since the arrival of the shock can be chosen to correspond as the reference point for when the fringe record starts to change, and since the VISAR is only working as a displacement interferometer for an initialτ /2 interval, the velocity is shifted to reflect this [30].

This type of simple VISAR setup has been constructed in the Caltech shock dynamics lab, and is shown in Figure 3.12. This VISAR was constructed in order to provide a wide range of interferometer delay times using etalon lengths of up to 350mm, in 50mmincrements. The interferometer delay time is calculated by examining the difference in time it takes for light to travel each path of the

interferometer and results in the well known form of τ= 2L c n−1 n , (3.10)

whereLis the length of the delaying medium, andnis its index of refraction.