Heterodyne transverse velocimetry for pressure-shear plate impact experiments

Christian Kettenbeil

, Michael Mello

, Moriah Bischann

, and

Guruswami Ravichandran

Citation:

Journal of Applied Physics

123

, 125902 (2018); doi: 10.1063/1.5023007

View online:

https://doi.org/10.1063/1.5023007

View Table of Contents:

http://aip.scitation.org/toc/jap/123/12

Published by the

American Institute of Physics

Heterodyne transverse velocimetry for pressure-shear plate impact

experiments

Christian

Kettenbeil,

Michael

Mello,

Moriah

Bischann,

and Guruswami

Ravichandran

Division of Engineering and Applied Science, California Institute of Technology, 1200 E. California Blvd.,

Pasadena, California 91125, USA

(Received 19 January 2018; accepted 10 March 2018; published online 29 March 2018)

Pressure-shear plate impact experiments have traditionally relied on free space beam interferometers

to measure transverse and normal particle velocities at the rear surface of the target plate. Here, we

present two different interferometry schemes that leverage heterodyne techniques, which enable the

simultaneous measurement of normal and transverse velocities using short-time Fourier transforms.

Both techniques rely on diffracted 1st order beams that are generated by a specular, metallic grating

deposited on the rear surface of the target plate. The diffracted beam photonic Doppler velocimetry

technique interferes each 1st order beam with a reference of slightly higher wavelength to create a

constant carrier frequency at zero particle velocity. The second technique interferes the 1st order

beams with each other and employs an acousto-optic frequency shifter on the

1st order beam to cre-

ate a heterodyne transverse velocimeter. For both interferometer techniques, the 0th order beam is

interfered in a heterodyne photonic Doppler velocimetry arrangement to obtain a measurement of the

normal particle velocity. An overview of both configurations is presented along with a derivation of

the interferometer sensitivities to transverse and normal particle velocities as well as design guidelines

for the optical system. Results from normal impact experiments conducted on Y-cut quartz are pre-

sented as the experimental validation of the two proposed techniques.

Published by AIP Publishing.

https://doi.org/10.1063/1.5023007

I. INTRODUCTION

The measurement of plane waves involving both longi-

tudinal and transverse velocity components is of particular

importance for the study of material strength at high strain

rates (

) and pressures ranging from hundreds of

MPa to several TPa. These conditions arise in, among others:

pressure-shear plate impact (PSPI) experiments,

dynami-

cally loaded anisotropic crystals,

laser-generated shear

waves,

and magnetically applied pressure-shear experi-

ments (MAPS).

Traditional PSPI experiments rely on the

transverse displacement interferometer (TDI)

for the mea-

surement of in-plane displacement histories. Recently, this

technique has been extended to an all fiber-optic configura-

tion.

Alternative schemes have leveraged dual VISAR

(Velocity Interferometer System for Any Reflector) arrange-

ments

that utilize normal and angled probes to measure

transverse velocity components. The main disadvantage of

this technique is that the fringe constant, as determined by

the etalon delay leg, is set to measure a superposition of both

normal and transverse particle velocities which generally

differ by an order of magnitude. Hence, the dual VISAR

approach cannot realize the full potential of the VISAR inter-

ferometry technique for PSPI experiments.

In recent years, there has been a paradigm shift towards

the application of PDV (photonic Doppler velocimetry) for

normal velocity measurements.

Along with the change in

instrumentation came the utilization of robust short-time

Fourier transform analysis techniques that are inherently

more immune to signal noise than previously used phase-

based methods and can therefore tolerate more light loss dur-

ing an experiment. The frequency-based approach is also

largely immune to amplitude modulation of the interferome-

ter signals and does not depend on normalized (amplitude

corrected) fringe records to extract frequency information, as

required when processing a single (unheterodyned) interfer-

ometer signal.

A limitation of “standard” (unheterodyned) PDV is the

inability of the technique to derive temporally resolved mea-

surements of low particle velocities from fringe records or

even partial fringes with correspondingly low signal frequen-

cies. This limitation in temporal resolution leads to inaccura-

cies and signal processing artifacts as demonstrated by the

discrepancy between a synthetic ramp velocity input pulse

and its measured result depicted in Fig.

1(a)

. A heterodyned

interferometer signal exhibits a carrier frequency

at zero

target velocity as depicted by the ramp wave frequency spec-

trum in Fig.

1(b)

. The increased frequency enables the use

of shorter time windows for the Fourier analysis and thus

provides a high temporal resolution even at low velocities.

While information at low velocities is not always required

for traditional normal plate impact experiments, it is abso-

lutely crucial for measuring transverse velocities in PSPI

experiments, which are typically below 50 m/s.

The main goal of this work is to extend heterodyne PDV

techniques, with their robust frequency-based analysis meth-

ods, to transverse interferometers utilized in PSPI

and mag-

netically applied pressure-shear experiments.

Two different

approaches were pursued to introduce a carrier frequency

in transverse velocimetry signals. Both techniques rely on

Electronic mail: ckb@caltech.edu

0021-8979/2018/123(12)/125902/14/$30.00

Published by AIP Publishing.

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, 125902-1

JOURNAL OF APPLIED PHYSICS

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diffracted 1st order beams generated by a specular, metallic

grating deposited on the rear surface of the target plate. The

diffracted beam photonic Doppler velocimetry (DPDV) tech-

nique interferes each 1st order beam with a reference laser

adjusted to a slightly higher wavelength. An additional bene-

fit of this transverse velocimeter lies in the independent mea-

sure of the normal velocity record that can be obtained by

decoupling the normal motion from the diffracted order sig-

nals. The second technique, called the heterodyne transverse

velocimeter (HTV), sends the

1st diffracted order through

an acousto-optic frequency shifter to create a carrier fre-

quency upon interference with the –1st order beam. In a sim-

ilar fashion to the transverse displacement interferometer,

this approach provides a pure measurement of transverse

motion. A measurement of the normal particle velocity is

obtained from a heterodyne PDV arrangement employing

the reflected 0th order diffracted beam. The strengths and

limitations of each interferometer design are addressed and

the techniques are compared by examining fringe records

obtained from normal impact validation experiments con-

ducted on Y-cut quartz.

II. OPTICAL DESIGN

Collecting diffracted or scattered light at an angle from

the surface normal, to measure in-plane transverse displace-

ments or velocities, poses a set of unique challenges in PSPI

experiments that are not encountered in normal plate impact

experiments. Normal displacement accumulated over the

course of the experiment causes decentering of the diffracted

beams at the receiving fiber-optic probes resulting in a rapid

loss of light intensity. Light loss is further exacerbated by

small tilt angles between the impacted surfaces of the flyer

and target plates. Analyzing the geometrical effects of target

tilt and normal displacement of the target surface can provide

valuable insights into a suitable optical design. The optical

design software Zemax was applied to investigate and quan-

tify light loss due to both of these effects during PSPI experi-

ments. The normal displacement during a PSPI experiment

will depend on the impact velocity, experiment duration, and

material response, resulting in varying optimal designs for

different experiments. However, impact tilts of up to 2 mrad

(0.11

) are considered typical in PSPI experiments and

should lie within the light loss tolerance exhibited by the opti-

cal system.

A. Probe design

Figure

shows two optical systems that were investi-

gated for their tolerance to normal displacement and tilt

of the target plate’s rear surface. The calculation of the cou-

pling efficiency requires the computation of an overlap inte-

gral between the electric field that impinges on the fiber-optic

core and the mode that can propagate in the utilized single

mode (SM) fiber. However, many qualitative trends can be

explained by appealing to geometrical optics.

FIG. 1. Frequency spectrum over time

for a ramp velocity input pulse (dashed

line) with inferred velocity for (a)

“standard” and (b) heterodyne PDV.

A Hamming window with a duration

15 ns was employed for the fre-

quency analysis.

FIG. 2. Geometrical analysis of light coupling in fiber-optic transverse inter-

ferometers for focused (a) and (b) and collimated (c) and (d) optical designs

subject to normal displacements

D

and tilt

125902-2 Kettenbeil

etal.

J. Appl. Phys.

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1. Geometrical analysis of optical system

Figure

2(a)

shows a fiber-optic configuration using focus-

ing probes, which are commonly utilized in normal plate

impact experiments.

The advantage of a focused optical sys-

tem is its insensitivity to small rotations of the target rear sur-

face, as highlighted in Fig.

2(b)

. The limitations of using this

approach for transverse measurements become immediately

apparent in Fig.

2(a)

, which highlights how quickly a dif-

fracted or scattered beam is decentered with respect to the

optical axis of the receiving probe upon normal motion of

the target. Figure

2(a)

also indicates that a larger spot size on

the target rear surface, corresp

onding to a longer working dis-

tance

, increases the tolerance to normal displacement. The

natural extension of this principle is to introduce a collimated

light system, which is shown in Fig.

2(c)

.Byreducingthe

beam diameter of the source probe, the diffracted beam will

decenter, with respect to the optical axis of the receiving

probe, without a reduction in light intensity at the fiber core

until the decentered beam is vignetted by the edge of the

receiving lens. The disadvantage of a collimated optical sys-

tem is emphasized in Fig.

2(d)

. Any tilt angle

of the target

rear surface will introduce a lateral translation of the focused

spot

from the fiber-optic core, which has a diameter of

8.2

m for standard

1550 nm wavelength single-mode

fiber. One way to alleviate this concern is to utilize a source

probe lens with a short focal length

resulting in a small

source beam diameter. This leads to an enlarged focused spot

size at the focal point of the receiving probe, which is larger

than the fiber-optic core resulting in light coupling even when

the center of the light distribution is displaced laterally by

This approach of increasing the system’s tolerance to tilt

comes at the expense of lower overall coupling efficiency.

However, this does not pose a limitation for the systems pre-

sented here, as light collected by the angled probes is close

to the damage threshold of the photodetectors, which limits

the usable light intensity in the employed interferometer sys-

tems. Another factor that has to be taken into account with

collimated optical systems is that a light beam can only stay

collimated over a finite distance. Assuming Gaussian beam

propagation, the collimation distance corresponds to the con-

focal parameter

, given by

;

(1)

where

is the Rayleigh range parameter and

represents

the beam waist radius. Equation

(1)

highlights the increasing

importance of the Rayleigh range with smaller beam sizes.

The collimated source beam used in the final experimental

configuration has a beam diameter of 280

m, which yields a

Rayleigh range

40 mm, corresponding to an 80 mm col-

limation distance. In order to avoid reductions in coupling

efficiency, the distance between the source and receiving

lens should be kept below this value. In contrast to focusing

systems, collimated designs experience no light loss due to

the depth of field of the employed probe lenses for

Now that the geometrical effects have been established,

the conflicting nature of the requirements for designs that

accept large tilt angles and have a high tolerance to normal

motion of the target plate becomes evident. A short focal

length of the receiving lens will yield an increased tolerance

to tilt, while a receiving lens with a long focal length will

result in an increased tolerance to decentering from the accu-

mulated normal displacement.

2. Optical simulations

Further progress towards the optical design requires a

more quantitative comparison of several optical configurations.

Optical simulations that propagate electric fields (Zemax

Physical Optics Propagation feature) were carried out to com-

pute the fiber coupling efficiency for varying amounts of nor-

mal displacement and target tilt. The fiber-optic lenses for the

optical simulations were chosen based on typical PDV probes

used for normal plate impact experiments.

Geometrical and

optical properties of aspheric lenses with a focal length of

1.4 mm, 6.2 mm, and 11 mm were sourced from Thorlabs

and used as input for the optical simulations. Focusing probes

were modeled by a collimator pair of

6.2 mm aspheric

lenses for which the spot size at the rear target surface was

minimized by adjusting the spacing of the lenses along the

optical axis.

The coupling efficiencies between the source and the

receiving side probes for two focused and two collimated opti-

cal configurations are shown in Fig.

. Focused designs are

characterized by their working distance

, whereas collimated

designs are designated by their source and receiving probe lens

focal length

. The final coupling efficiency for each receiving

side probe can be obtained by multiplying the results displayed

in Fig.

by the diffraction efficiency

, which depends on the

diffraction grating design and is described in Sec.

II B

.Figure

3(a)

shows, as mentioned in the previous geometrical analysis,

that focusing probes will suffer from a rapid loss of coupling

efficiency upon normal motion of the target. Considering the

immense light loss of the

100 mm focused design, it is not

advisable to use working distances at or below this value for

passive receiving probes. Figure

3(a)

confirms that a focused

configuration with a larger working distance

is less sensitive

toward normal displacements of the target. As expected, the

light loss designed into the collimated configurations yields a

lower initial coupling efficiency. However, the small relative

change of efficiency with target normal motion makes the col-

limated configuration more suited to transverse interferometry

applications. Typical diagnostic systems can compensate the

lower initial coupling efficiencies with a higher source beam

intensity.

The importance of achieving a low impact tilt during

PSPI experiments with spectrally reflective surfaces is demon-

strated in Fig.

3(b)

. As previously mentioned, especially short

focal length focused configurations offer a higher tolerance to

tilt than collimated systems. However, Fig.

3(b)

confirms the

result of the geometric analysis that using a short focal length

source lens in a collimated system can provide a suitable tilt

tolerance, which can surpass the absolute efficiency of a

250 mm focused systems at tilt angles above 1.5 mrad

(0.085

) and provide a much more constant light coupling. As

a result of this analysis, a probe design that incorporates a

1.4 mm collimated source lens with a

6.2 mm receiving

125902-3 Kettenbeil

etal.

J. Appl. Phys.

123

, 125902 (2018)