Analysis of focused laser differential interferometry

B. E. Schmidt; J. E. Shepherd

doi:10.1364/AO.54.008459

Applied Optics
Vol. 54,
Issue 28,
pp. 8459-8472
(2015)
•https://doi.org/10.1364/AO.54.008459

Analysis of focused laser differential interferometry

B. E. Schmidt and J. E. Shepherd

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B. E. Schmidt and J. E. Shepherd, "Analysis of focused laser differential interferometry," Appl. Opt. 54, 8459-8472 (2015)

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Abstract

A computational method for predicting the output of a focused laser differential interferometer (FLDI) given an arbitrary density field is presented. The method is verified against analytical predictions and experimental data. The FLDI simulation software is applied to the problem of measuring Mack-mode wave packets in a hypervelocity boundary layer on a 5° half-angle cone. The software is shown to complement experiments by providing the necessary information to allow quantitative density fluctuation magnitudes to be extracted from experimental measurements.

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Divergence angle of prisms ( $σ$ )	2 arc min
$1 / e^{2}$ beam diameter at focusing lens ( $D_{4 σ}$ )	48 mm
Focal length of focusing lenses ( $f$ )	300 mm
Distance from focusing lens to focus ( $d$ )	515 mm
$λ$	532 nm

Configuration	$L_{jet}$	$z_{0}$
A	165	0
B	130	0
C	110	0
D	90	0
E	70	0
F	50	0
G	30	0
H	20	0
I	10	0
J	82.5	41.25
K	20	10
L	20	20
M	20	30
N	32.5	66.25

$M_{e}$	4.55
$T_{e}$	2105 K
$U_{e}$	4191 m/s
$p_{e}$	47.1 kPa
Re/m	$4.76 \times 10^{6} / m$
$ρ_{e}$	$0.0777 kg / m^{3}$

$ρ_{SF}$	$2.276 \times 10^{- 20} kg / m^{3}$
$A$	$- \ln 0.01 = 4.6$
$L$	$14 π / α_{r} = 20.8 mm$
$x_{0}$	$710 mm - l = 689.2 mm$
$c_{r}$	3633 m/s
$α_{i}$	−0.0488/mm
$α_{r} = k$	2.116/mm
$ω = 2 π f = c_{r} α_{r}$	$7.697 \times 10^{6} rad / s$

Case No.	$α_{r}$ [1/mm]	$c_{r}$ [m/s]	$f$ [Hz]	% Error
1	2.116	3633	$1.22 \times 10^{6}$	0.0
2	0.4	3633	$2.31 \times 10^{5}$	4.0
3	7	3633	$4.05 \times 10^{6}$	−26
4	30	3633	$1.73 \times 10^{7}$	−94
5	2.116	2500	$8.42 \times 10^{5}$	0.0
6	2.116	5000	$1.68 \times 10^{6}$	0.0

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Applied Optics