Design and evaluation of a THz time domain imaging system using standard optical design software

Claudia Brückner; Boris Pradarutti; Ralf Müller; Stefan Riehemann; Gunther Notni; Andreas Tünnermann

doi:10.1364/AO.47.004994

Applied Optics
Vol. 47,
Issue 27,
pp. 4994-5006
(2008)
•https://doi.org/10.1364/AO.47.004994

Design and evaluation of a THz time domain imaging system using standard optical design software

Claudia Brückner, Boris Pradarutti, Ralf Müller, Stefan Riehemann, Gunther Notni, and Andreas Tünnermann

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Claudia Brückner, Boris Pradarutti, Ralf Müller, Stefan Riehemann, Gunther Notni, and Andreas Tünnermann, "Design and evaluation of a THz time domain imaging system using standard optical design software," Appl. Opt. 47, 4994-5006 (2008)

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Abstract

A terahertz (THz) time domain imaging system is analyzed and optimized with standard optical design software (ZEMAX). Special requirements to the illumination optics and imaging optics are presented. In the optimized system, off-axis parabolic mirrors and lenses are combined. The system has a numerical aperture of 0.4 and is diffraction limited for field points up to $4 mm$ and wavelengths down to $750 μm$ . ZEONEX is used as the lens material. Higher aspherical coefficients are used for correction of spherical aberration and reduction of lens thickness. The lenses were manufactured by ultraprecision machining. For optimization of the system, ray tracing and wave-optical methods were combined. We show how the ZEMAX Gaussian beam analysis tool can be used to evaluate illumination optics. The resolution of the THz system was tested with a wire and a slit target, line gratings of different period, and a Siemens star. The behavior of the temporal line spread function can be modeled with the polychromatic coherent line spread function feature in ZEMAX. The spectral and temporal resolutions of the line gratings are compared with the respective modulation transfer function of ZEMAX. For maximum resolution, the system has to be diffraction limited down to the smallest wavelength of the spectrum of the THz pulse. Then, the resolution on time domain analysis of the pulse maximum can be estimated with the spectral resolution of the center of gravity wavelength. The system resolution near the optical axis on time domain analysis of the pulse maximum is $1 line pair / mm$ with an intensity contrast of 0.22. The Siemens star is used for estimation of the resolution of the whole system. An eight channel electro-optic sampling system was used for detection. The resolution on time domain analysis of the pulse maximum of all eight channels could be determined with the Siemens star to be $0.7 line pairs / mm$ .

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Wavelength ( $μm$ )	$w_{0} (mm)$	Divergence (°)	Divergence @ $2 w_{0} (°)$	Required NA to Avoid Beam Clipping	${w_{0}}^{'} (mm)$	Image-Side Gaussian Beam Position (mm)	Focal Depth (mm)
200	1.5	2.43	4.85	0.085	1.23	3.24	38.63
300	1.5	3.64	7.25	0.126	1.27	1.48	26.52
750	1.5	9.04	17.7	0.30	1.29	0.00	10.84
1000	1.5	11.98	23.0	0.39	1.30	$- 0.14$	8.15
3000	1.5	32.48	51.9	0.79	1.32	$- 0.29$	2.76

Analyzed Measurement Signal	Measurement @ $0.5 I_{\max}$	ZEMAX FFT LSF @ $0.5 I_{\max}$	Absolute Deviation ( $mm$ ) @ $0.5 I_{\max}$	Deviation (%) @ $0.5 I_{\max}$	Measurement @ $0.135 I_{\max}$	ZEMAX FFT LSF @ $0.135 I_{\max}$	Absolute Deviation (mm) @ $0.135 I_{\max}$	Deviation (%) @ $0.135 I_{\max}$
Temporal, Pulse Maximum	1.12 ( $500 μm$ )	0.90	0.22	19.64	2.06 ( $500 μm$ )	1.56	0.5	24.27
$335 μm$	0.60 ( $200 μm$ )	0.38	0.22	36.67	0.95 ( $200 μm$ )	0.73	0.22	23.16
$776 μm$ (CG)	1.13 ( $500 μm$ )	0.84	0.29	26.00	1.69 ( $500 μm$ )	1.36	0.33	19.53
$1134 μm$ (peak)	1.55 ( $500 μm$ )	1.24	0.31	20.00	2.33 ( $500 μm$ )	1.96	0.37	15.88
$2949 μm$	4.08 ( $2 mm$ )	3.19	0.89	21.81	6.07 ( $2 mm$ )	5.04	1.03	16.97

Analyzed Measurement Signal	Measurement @ $0.5 I_{\max}$	ZEMAX FFT LSF @ $0.5 I_{\max}$	Absolute Deviation (mm) @ $0.5 I_{\max}$	Deviation (%) @ $0.5 I_{\max}$	Measurement @ $0.135 I_{\max}$	ZEMAX FFT LSF @ $0.135 I_{\max}$	Absolute Deviation (mm) @ $0.135 I_{\max}$	Deviation (%) @ $0.135 I_{\max}$
Temporal, Pulse Maximum	1.12 ( $500 μm$ )	0.90	0.22	19.64	2.06 ( $500 μm$ )	1.56	0.5	24.27
$335 μm$	0.39 ( $200 μm$ )	0.38	0.01	2.56	0.71( $200 μm$ )	0.72	$- 0.01$	$- 1.41$
$658 μm$ (CG)	0.87 ( $500 μm$ )	0.72	0.15	17.24	1.43 ( $500 μm$ )	1.17	0.26	18.18
$838 μm$ (peak)	1.07 ( $500 μm$ )	0.91	0.16	14.95	1.72 ( $500 μm$ )	1.46	0.26	15.12
$3072 μm$	2.69 ( $2 mm$ )	3.32	$- 0.63$	$- 18.98$	4.48 ( $2 mm$ )	5.25	$- 0.77$	$- 17.19$

Analyzed Measurement Signal	Boundary Frequency Determined by the Measurement ( $LP / mm$ )	Intensity Modulation at the Measured Boundary Frequency	Boundary Frequency Determined by the FFT MTF of ZEMAX ( $LP / mm$ ) Object space	Intensity Modulation of the ZEMAX Boundary Frequency, Tangential
$λ = 297 μm$ (pixel 4)	1	$M = 1$	2.084	$M = 0$
$λ = 658 μm$ (pixel 4)	0.67	$M = 0.34$	0.945	$M = 0$
$λ = 838 μm$ (pixel 4)	0.5	$M = 0.52$	0.742	$M = 0$
$λ = 3072 μm$ (pixel 4)	0.25	$M = 0.23$	0.202	$M = 0$
Time Domain Analysis of the Pulse Maximum, pixel 4	1	$M = 0.22$	2.076	$M = 0$
Time Domain Analysis of the Pulse Maximum, pixel 8	0.67	$M = 0.23$	2.097	$M = 0$

Wavelength ( $μm$ )	$w_{0} (mm)$	Divergence (°)	Divergence @ $2 w_{0} (°)$	Required NA to Avoid Beam Clipping	${w_{0}}^{'} (mm)$	Image-Side Gaussian Beam Position (mm)	Focal Depth (mm)
200	1.5	2.43	4.85	0.085	1.23	3.24	38.63
300	1.5	3.64	7.25	0.126	1.27	1.48	26.52
750	1.5	9.04	17.7	0.30	1.29	0.00	10.84
1000	1.5	11.98	23.0	0.39	1.30	$- 0.14$	8.15
3000	1.5	32.48	51.9	0.79	1.32	$- 0.29$	2.76

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Applied Optics