Strain field measurement by transverse digital holography

Karl A. Stetson

doi:10.1364/AO.54.006065

Applied Optics
Vol. 54,
Issue 19,
pp. 6065-6070
(2015)
•https://doi.org/10.1364/AO.54.006065

Strain field measurement by transverse digital holography

Karl A. Stetson

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Karl A. Stetson, "Strain field measurement by transverse digital holography," Appl. Opt. 54, 6065-6070 (2015)

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Abstract

The technique generally referred to as speckle correlation interferometry may be described as transverse digital holography when phase stepping is applied, because phase stepping allows complete maps to be obtained of the transverse displacement of an object surface. This paper describes the analysis of these maps to obtain surface strain by fitting data to flat surfaces for least square error within sections of the map. Examples are shown for measuring rotation, thermal contraction, and strains around the tip of a notch. Only uniaxial strain is measured; however, the possibility for biaxial measurement is considered.

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a, $strain = d L x / d x$ ; expected $value = 0$ ; $average = 1.41 E - 6$
$1.8 E - 6$	$- 1.1 E - 6$	$2.7 E - 6$	$0.70 E - 6$	$0.25 E - 6$
$0.67 E - 6$	$1.3 E - 6$	$2.8 E - 6$	$1.6 E - 6$	$- 0.38 E - 6$
$- 0.69 E - 6$	$4.0 E - 6$	$0.73 E - 6$	$2.1 E - 6$	$3.4 E - 6$
$1.3 E - 6$	$3.6 E - 6$	$- 0.93 E - 6$	$- 0.54 E - 6$	$4.8 E - 6$
b, rotation and $shear = d L x / d y$ ; expected $value = - 500 E - 6$ ; $average = - 521 E - 6$
$- 520 E - 6$	$- 521 E - 6$	$- 522 E - 6$	$- 524 E - 6$	$- 521 E - 6$
$- 521 E - 6$	$- 521 E - 6$	$- 520 E - 6$	$- 521 E - 6$	$- 524 E - 6$
$- 517 E - 6$	$- 519 E - 6$	$- 520 E - 6$	$- 522 E - 6$	$- 526 E - 6$
$- 519 E - 6$	$- 516 E - 6$	$- 518 E - 6$	$- 519 E - 6$	$- 519 E - 6$

a, Thermal contraction from 35°C to 33°C $Average = 47.7 E - 6$ ; $COE = 23.85 ppm / ° C$
$- 48.4 E - 6$	$- 47.4 E - 6$	$- 46.8 E - 6$	$- 46.8 E - 6$	$- 47.0 E - 6$
$- 47.7 E - 6$	$- 45.6 E - 6$	$- 47.7 E - 6$	$- 47.4 E - 6$	$- 47.2 E - 6$
$- 46.6 E - 6$	$- 47.9 E - 6$	$- 48.2 E - 6$	$- 47.8 E - 6$	$- 50.6 E - 6$
$- 47.6 E - 6$	$- 47.0 E - 6$	$- 48.5 E - 6$	$- 48.0 E - 6$	$- 49.3 E - 6$
b, Thermal contraction from 33°C to 31°C $Average = 47.5 E - 6$ ; $COE = 23.75 ppm / ° C$
$- 48.4 E - 6$	$- 45.5 E - 6$	$- 45.0 E - 6$	$- 45.1 E - 6$	$- 47.7 E - 6$
$- 47.9 E - 6$	$- 44.7 E - 6$	$- 45.4 E - 6$	$- 47.2 E - 6$	$- 47.5 E - 6$
$- 48.2 E - 6$	$- 48.0 E - 6$	$- 48.6 E - 6$	$- 46.8 E - 6$	$- 51.2 E - 6$
$- 48.1 E - 6$	$- 48.1 E - 6$	$- 49.3 E - 6$	$- 47.8 E - 6$	$- 49.8 E - 6$
c, Thermal contraction from 31 to 29°C $Average = 51.0 E - 6$ ; $COE = 25.5 ppm / ° C$
$- 52.3 E - 6$	$- 49.0 E - 6$	$- 47.2 E - 6$	$- 48.0 E - 6$	$- 49.6 E - 6$
$- 52.6 E - 6$	$- 49.4 E - 6$	$- 49.2 E - 6$	$- 49.2 E - 6$	$- 49.7 E - 6$
$- 52.7 E - 6$	$- 51.6 E - 6$	$- 51.4 E - 6$	$- 52.4 E - 6$	$- 53.9 E - 6$
$- 53.1 E - 6$	$- 50.5 E - 6$	$- 53.3 E - 6$	$- 51.4 E - 6$	$- 54.2 E - 6$
d, Thermal contraction from 29°C to 27°C $Average = 48.4 E - 6$ ; $COE = 24.2 pm / ° C$
$- 47.8 E - 6$	$- 46.8 E - 6$	$- 46.4 E - 6$	$- 47.3 E - 6$	$- 48.9 E - 6$
$- 47.7 E - 6$	$- 47.7 E - 6$	$- 47.8 E - 6$	$- 49.3 E - 6$	$- 49.8 E - 6$
$- 47.5 E - 6$	$- 47.6 E - 6$	$- 47.6 E - 6$	$- 50.1 E - 6$	$- 50.4 E - 6$
$- 49.2 E - 6$	$- 47.6 E - 6$	$- 49.0 E - 6$	$- 49.4 E - 6$	$- 50.3 E - 6$

a, Notched sample stress relief—strain in $x$ direction
$24.8 E - 6$	$23.5 E - 6$	$5.0 E - 6$	$11.2 E - 6$	$25.0 E - 6$
$63.0 E - 6$	$96.2 E - 6$	$96.9 E - 6$	$99.4 E - 6$	$75.2 E - 6$
$49.8 E - 6$	$69.6 E - 6$		$74.5 E - 6$	$63.8 E - 6$
$- 1.2 E - 6$	$- 44.7 E - 6$		$- 57.4 E - 6$	$- 1.0 E - 6$
b, Notched sample stress relief—rotation and shear
$73.8 E - 6$	$17.1 E - 6$	$- 39.2 E - 6$	$- 89.1 E - 6$	$- 152.4 E - 6$
$176.2 E - 6$	$129.1 E - 6$	$- 17.3 E - 6$	$- 187.0 E - 6$	$- 260.2 E - 6$
$309.2 E - 6$	$404.9 E - 6$		$- 566.9 E - 6$	$- 429.6 E - 6$
$396.8 E - 6$	$454.9 E - 6$		$- 581.8 E - 6$	$- 528.0 E - 6$

a, Notched sample stress relief—strain in $y$
$107.4 E - 6$	$171.4 E - 6$	$207.5 E - 6$	$157.6 E - 6$	$96.2 E - 6$
$84.1 E - 6$	$154.9 E - 6$	$227.8 E - 6$	$131.4 E - 6$	$77.4 E - 6$
$97.2 E - 6$	$188.0 E - 6$		$168.0 E - 6$	$92.1 E - 6$
$141.6 E - 6$	$225.7 E - 6$		$232.0 E - 6$	$132.0 E - 6$
b, Notched sample stress relief—rotation and shear
$- 255 E - 6$	$- 157 E - 6$	$56.5 E - 6$	$236.0 E - 6$	$300.0 E - 6$
$- 299 E - 6$	$- 251 E - 6$	$84.9 E - 6$	$309.6 E - 6$	$347.5 E - 6$
$- 339 E - 6$	$- 362 E - 6$		$375.0 E - 6$	$387.9 E - 6$
$- 407 E - 6$	$- 480 E - 6$		$489.3 E - 6$	$451.6 E - 6$

a, Notched sample stress relief—strain in $y$ at left edge
$- 239 E - 6$	$- 177 E - 6$	$- 121 E - 6$	$- 71.6 E - 6$	$- 25.7 E - 6$
$- 247 E - 6$	$- 182 E - 6$	$- 126 E - 6$	$- 75.9 E - 6$	$- 27.6 E - 6$
$- 247 E - 6$	$- 181 E - 6$	$- 125 E - 6$	$- 73.9 E - 6$	$- 22.4 E - 6$
$- 244 E - 6$	$- 181 E - 6$	$- 123 E - 6$	$- 68.5 E - 6$	$- 12.6 E - 6$
b, Notched sample stress relief—strain and shear at left edge
$- 371 E - 6$	$- 387 E - 6$	$- 392 E - 6$	$- 399 E - 6$	$- 399 E - 6$
$- 435 E - 6$	$- 441 E - 6$	$- 441 E - 6$	$- 442 E - 6$	$- 441 E - 6$
$- 499 E - 6$	$- 496 E - 6$	$- 491 E - 6$	$- 488 E - 6$	$- 484 E - 6$
$- 562 E - 6$	$- 553 E - 6$	$- 542 E - 6$	$- 539 E - 6$	$- 535 E - 6$

Abstract

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Figures (8)

Tables (5)

Equations (11)

Applied Optics