Dynamic focal shift and extending depth of focus based on the masking of the illuminating beam and using an adjustable axicon

Svetlana N. Khonina; Andrey V. Ustinov; Alexey P. Porfirev

doi:10.1364/JOSAA.36.001039

Dynamic focal shift and extending depth of focus based on the masking of the illuminating beam and using an adjustable axicon

Svetlana N. Khonina, Andrey V. Ustinov, and Alexey P. Porfirev

Journal of the Optical Society of America A
Vol. 36,
Issue 6,
pp. 1039-1047
(2019)
•https://doi.org/10.1364/JOSAA.36.001039

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Svetlana N. Khonina, Andrey V. Ustinov, and Alexey P. Porfirev, "Dynamic focal shift and extending depth of focus based on the masking of the illuminating beam and using an adjustable axicon," J. Opt. Soc. Am. A 36, 1039-1047 (2019)

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- Diffraction and Gratings
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About this Article
History
- Original Manuscript: February 26, 2019
- Manuscript Accepted: April 23, 2019
- Published: May 22, 2019

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Abstract

We investigate several methods of focus shift and focus extension in detail. These methods are divided into two groups: (1) changing the radius of the illuminating beam and/or limiting diaphragm; and (2) adding an optical system with an adjustable element (lens or axicon). In the cases of a planar and Gaussian illuminating beam, values of the focus position and depth of focus (DOF) are calculated theoretically and numerically, depending on the beam radius. In addition, theoretical and numerical evaluations of displacement and DOF increase for the focusing system with the adjustable lens or axicon obtained. We show that these methods for changing the parameters of the focal area provide flexibility and efficiency in the control of its characteristics. Recommendations about possible applications in which such control is important are formulated on the basis of the results obtained.

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$σ$ , mm	5	3	2	1.5
Theoretical maximum position calculated with Eq. (6) $z_{\max}^{g s}$ , mm	499.99	499.96	499.78	499.29
Calculated maximum position, mm	500	500	499.6	499.2
Theoretical DOF calculated with Eq. (12) ${DOF}_{g s}$ , mm	3.39	9.41	21.17	37.63
Calculated DOF, mm	3.4	9.4	21.16	37.58

$R$ , mm	5	3	2	1.5
Theoretical maximum position calculated with Eq. (23) $z_{\max}^{pl}$ , mm	499.93	499.47	497.31	491.50
Calculated maximum position, mm	500	499.6	497.2	492
Theoretical DOF calculated with Eq. (19) ${DOF}_{pl}$ , mm	$504.75 - 495.33 = 9.42$	$513.43 - 487.26 = 26.17$	$531.26 - 472.21 = 59.05$	$558.42 - 452.64 = 105.78$
Calculated DOF, mm	9.43	26.13	58.35	101.63

Axicon Parameter $α_{0}$	$\pm 0.0001$	$\pm 0.0002$	$\pm 0.0003$
Theoretical maximum position calculated with Eq. (37), $z_{\max}^{g a x}$ , mm	508/492	518.4/482.8	530.4/472
Calculated maximum position, mm	509.81/490.56	520.02/481.47	530.64/472.71
Theoretical DOF calculated with Eqs. (39), (40), DOFgax, mm	12.56/12.08	20.62/18.71	33.2/28.1
Calculated DOF, mm	$517.22 - 506.44 = 10.78 / 493.71 - 483.89 = 9.82$	$535.67 - 513.06 = 22.61 / 487.59 - 468.78 = 18.81$	$555.49 - 519.84 = 35.65 / 481.62 - 454.59 = 27.03$

Value of Parameter $α_{0}$	$\pm 0.0001$	$\pm 0.0002$	$\pm 0.0003$
Theoretical maximum position calculated with Eq. (49), $z_{\max}^{a x}$ , mm	517.67/483.5	529.46/473.64	541.15/464.66
Calculated maximum position, mm	513.2/486.4	527.2/474.4	541.6/463.2
Theoretical DOF calculated with Eq. (52), ${DOF}_{a x}$ , mm	$522.47 - 514.01 = 8.46$ $486.73 - 479.38 = 7.35$	$537.69 - 524.84 = 12.85$ $477.40 - 467.25 = 10.15$	$552.98 - 535.68 = 17.3$ $468.78 - 456.29 = 12.49$
Calculated DOF, mm	27.83/25	30.24/24.43	33.72/24.53

Illuminating Beam Radius R, mm	3	3,5	4
Theoretical maximum position calculated with Eq. (49) $z_{\max}^{a x}$ , mm	529.46/473.64	524.08/478.04	520.29/481.23
Calculated maximum position, mm	527.2/474.4	523.2/478	520.4/480.8
Theoretical DOF calculated with Eq. (52) ${DOF}_{a x}$ , mm	$537.69 - 524.84 = 12.85$ $477.40 - 467.25 = 10.15$	$530.73 - 520.58 = 10.15$ $480.98 - 472.63 = 8.35$	$525.84 - 517.54 = 8.3$ $483.61 - 476.58 = 7.03$
Calculated DOF, mm	30.24/24.43	22.2/18.5	17.1/14.58

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