Study on angular distribution of differential photoacoustic cross-section and its implication in source size determination

Anuj Kaushik; Deepak Sonker; Ratan K. Saha

doi:10.1364/JOSAA.36.000387

Journal of the Optical Society of America A
Vol. 36,
Issue 3,
pp. 387-396
(2019)
•https://doi.org/10.1364/JOSAA.36.000387

Study on angular distribution of differential photoacoustic cross-section and its implication in source size determination

Anuj Kaushik, Deepak Sonker, and Ratan K. Saha

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Anuj Kaushik, Deepak Sonker, and Ratan K. Saha, "Study on angular distribution of differential photoacoustic cross-section and its implication in source size determination," J. Opt. Soc. Am. A 36, 387-396 (2019)

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Abstract

Angular distribution of a differential photoacoustic cross-section (DPACS) has been examined for various nonspherical axisymmetric particles. The DPACS as a function of measurement angle has been computed for spheroidal particles with varying aspect ratios and fitted with a tri-axes ellipsoid form factor model to extract shape parameters. Similar study has been carried out for normal and pathological red blood cells, and fitting has been performed with the tri-axes ellipsoid and finite cylinder form factor models to evaluate cellular morphology. It is found that an enhancement of the DPACS occurs as the surface area of the photoacoustic source normal to the direction of measurement is increased. It decreases as the thickness of the source along the same direction increases. For example, the DPACS for normal erythrocyte along the direction of symmetry is nearly 20 times greater than a pathological cell. Further, the first minimum appears slightly later ( $\approx 4 °$ ) for a healthy cell compared with that of a diseased cell. Shape information of spheroids can be precisely estimated by the first model. Both models provide accurate estimates of shape parameters for normal red blood cells (errors within 4%). It may be possible to assess cellular morphology from an angular profile of the DPACS using form factor models.

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Equations (19)

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$ρ$	$1005 kg / m^{3}$
$v$	1498 m/s
$μ$	$809.02 m^{- 1}$
$β$	$1.5 \times 10^{- 4} K^{- 1}$
$C_{P}$	$3.23 \times 10^{3} J {kg}^{- 1} K^{- 1}$
$I_{0}$	$1.51 \times 10^{12} J m^{- 2} s^{- 1}$

Objects	Volume ( ${μm}^{3}$ )	Shape Parameters
Spheroids	523.6	$b : a = 1 : 8$ , 1:4, 1:2, 1:1, 2:1, 4:1, 8:1
RBCs	104	$D = 7.65$ , $t / 2 = 0.70$ , $h / 2 = 1.42$ , $R_{e} = 0.5 D$ , $d = 0.7 D$ , $L = 19$
	105	$D = 6.37$ , $t / 2 = 1.36$ , $h / 2 = 1.47$ , $R_{e} = 0.5 D$ , $d = 0.7 D$ , $L = 19$
	104	$D = 6.54$ , $t / 2 = 0.21$ , $h / 2 = 1.16$ , $R_{e} = 0.5 D$ , $d = 0.7 D$ , $L = 19$

PA Source Spheroid	Nominal Values (μm)	Angular Range for Fitting	Estimated Values (μm)
			Tri-axes Ellipsoid
			$ϕ = 0 °$	$ϕ = 90 °$	Fitting Error (%)
$AR = 1 : 2$	$a = 6.93$	0–43°	$ϱ_{1} = 6.93$	5.83	0.48
	$a = 6.93$		$ϱ_{2} = 5.59$	6.93
	$b = 3.46$		$ϱ_{3} = 3.46$	3.46
$AR = 1 : 4$	$a = 8.72$	0–35°	$ϱ_{1} = 8.74$	7.70	0.23
	$a = 8.72$		$ϱ_{2} = 8.90$	8.74
	$b = 2.18$		$ϱ_{3} = 2.14$	2.14
$AR = 1 : 8$	$a = 10.96$	0–28°	$ϱ_{1} = 10.95$	10.41	0.08
	$a = 10.96$		$ϱ_{2} = 10.19$	10.95
	$b = 1.37$		$ϱ_{3} = 1.39$	1.39
$AR = 2 : 1$	$a = 4.36$	90–114°	$ϱ_{1} = 4.38$	3.84	0.26
	$a = 4.36$		$ϱ_{2} = 5.27$	4.38
	$b = 8.72$		$ϱ_{3} = 8.67$	8.67
$AR = 4 : 1$	$a = 3.46$	90–108°	$ϱ_{1} = 3.46$	2.85	0.10
	$a = 3.46$		$ϱ_{2} = 4.32$	3.46
	$b = 13.86$		$ϱ_{3} = 13.86$	13.86
$AR = 8 : 1$	$a = 2.75$	90–102°	$ϱ_{1} = 2.75$	2.75	0.10
	$a = 2.75$		$ϱ_{2} = 1.89$	2.75
	$b = 22.01$		$ϱ_{3} = 22.01$	22.01

PA Source	Nominal Values (μm)	Angular Range for Fitting	Estimated Values (μm)
			Tri-axes Ellipsoid			Finite Cylinder
			$ϕ = 0 °$	$ϕ = 90 °$	Fitting Error (%)	Estimates	Fitting Error (%)
Normal RBC	$R_{e} = 3.82$	0–38°	$ϱ_{1} = 3.65$	2.83	0.13	$Γ = 3.74$	1.0
	$t / 2 = 0.7$		$ϱ_{2} = 4.10$	3.65		$L = 2.19$
	$h / 2 = 1.42$		$ϱ_{3} = 1.88$	1.88		$L = 2.19$
Stomatocyte1	$R_{e} = 3.18$	0–34°	$ϱ_{1} = 3.76$	4.61	2.0	$Γ = 3.81$	1.8
	$t / 2 = 1.36$		$ϱ_{2} = 2.43$	3.76		$L = 2.11$
	$h / 2 = 1.47$		$ϱ_{3} = 1.82$	1.82		$L = 2.11$
Stomatocyte2	$R_{e} = 3.27$	0–33°	$ϱ_{1} = 3.67$	4.87	6.6	$Γ = 3.24$	7.4
	$t / 2 = 0.21$		$ϱ_{2} = 2.07$	3.67		$L = Not$
	$h / 2 = 1.16$		$ϱ_{3} = Not$	Not		converging
	$h / 2 = 1.16$		converging	converging		converging

$ρ$	$1005 kg / m^{3}$
$v$	1498 m/s
$μ$	$809.02 m^{- 1}$
$β$	$1.5 \times 10^{- 4} K^{- 1}$
$C_{P}$	$3.23 \times 10^{3} J {kg}^{- 1} K^{- 1}$
$I_{0}$	$1.51 \times 10^{12} J m^{- 2} s^{- 1}$

Abstract

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Figures (8)

Tables (4)

Equations (19)

Journal of the Optical Society of America A