Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters

Daniel M. de Juana; José E. Oti; Vidal F. Canales; Manuel P. Cagigal

doi:10.1364/JOSAA.20.002172

Journal of the Optical Society of America A
Vol. 20,
Issue 11,
pp. 2172-2178
(2003)
•https://doi.org/10.1364/JOSAA.20.002172

Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters

Daniel M. de Juana, José E. Oti, Vidal F. Canales, and Manuel P. Cagigal

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Daniel M. de Juana, José E. Oti, Vidal F. Canales, and Manuel P. Cagigal, "Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters," J. Opt. Soc. Am. A 20, 2172-2178 (2003)

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Abstract

A novel procedure to design axial and transverse superresolving pupil filters for the 4Pi-confocal microscope is presented. The method is based on the use of a series of figures of merit developed to describe the effect of inserting two identical filters in the two arms of the illumination path of the microscope. As a practical implementation, we have applied our method to obtain superresolving continuous phase-only filters. Different resolution-improving phase functions are shown for the transverse and the axial direction. These filters provided axial gain up to 1.3 and transverse gain up to 1.4 without an increase in sidelobes.

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Phase Function	a	b	$G_{A}$	$G_{T}$	S	$I_{lob}$
$a sin (2 π b ρ^{2})$	-3.592	-0.550	1.40	0.44	0.10	0.55
	1.997	1.318	1.14	0.93	0.08	0.14
	1.927	1.344	1.09	0.97	0.10	0.15
$a sin (2 π b ρ^{3})$	1.804	1.339	1.20	0.81	0.19	0.16
	2.004	1.310	1.30	0.70	0.12	0.14
	2.004	2.620	1.14	0.88	0.10	0.15
$a ρ^{3} + b ρ^{5}$	4.759	3.399	1.33	0.70	0.10	0.10
	-12.526	16.181	1.43	0.44	0.25	0.38

Phase Function	a	b	$G_{T}$	$G_{A}$	S	$I_{lob}$
$a sin (2 π b ρ)$	22.790	0.310	1.30	0.69	0.32	0.39
	54.542	0.291	1.40	0.60	0.19	0.42
$a sin (2 π b ρ^{2})$	2.800	1.425	1.19	0.863	0.11	0.13
$a ρ^{3} + b ρ^{5}$	25.129	-18.988	1.30	0.72	0.26	0.27
	61.453	-42.322	1.40	0.63	0.12	0.24
$a exp [- (ρ / b)^{2}]$	50.908	0.193	1.12	0.88	0.74	0.28
	207.178	0.184	1.14	0.86	0.69	0.30
$a sin (2 π ρ)$ $+ b sin (4 π ρ)$	-0.993	1.400	1.30	0.72	0.23	0.27
$a sin (2 π ρ^{2})$ $+ b sin (4 π ρ^{2})$	-1.465	1.462	1.17	0.90	0.10	0.09

Phase Function	a	b	$G_{A}$	$G_{T}$	S	$I_{lob}$
$a sin (2 π b ρ^{2})$	-3.592	-0.550	1.40	0.44	0.10	0.55
	1.997	1.318	1.14	0.93	0.08	0.14
	1.927	1.344	1.09	0.97	0.10	0.15
$a sin (2 π b ρ^{3})$	1.804	1.339	1.20	0.81	0.19	0.16
	2.004	1.310	1.30	0.70	0.12	0.14
	2.004	2.620	1.14	0.88	0.10	0.15
$a ρ^{3} + b ρ^{5}$	4.759	3.399	1.33	0.70	0.10	0.10
	-12.526	16.181	1.43	0.44	0.25	0.38

Phase Function	a	b	$G_{T}$	$G_{A}$	S	$I_{lob}$
$a sin (2 π b ρ)$	22.790	0.310	1.30	0.69	0.32	0.39
	54.542	0.291	1.40	0.60	0.19	0.42
$a sin (2 π b ρ^{2})$	2.800	1.425	1.19	0.863	0.11	0.13
$a ρ^{3} + b ρ^{5}$	25.129	-18.988	1.30	0.72	0.26	0.27
	61.453	-42.322	1.40	0.63	0.12	0.24
$a exp [- (ρ / b)^{2}]$	50.908	0.193	1.12	0.88	0.74	0.28
	207.178	0.184	1.14	0.86	0.69	0.30
$a sin (2 π ρ)$ $+ b sin (4 π ρ)$	-0.993	1.400	1.30	0.72	0.23	0.27
$a sin (2 π ρ^{2})$ $+ b sin (4 π ρ^{2})$	-1.465	1.462	1.17	0.90	0.10	0.09

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