Self-calibrated BFP-type apertometer for both dry and immersion lenses via grating projection reference

Bei Zhang; Cuiling Zhang

doi:10.1364/OL.438762

Optics Letters
Vol. 46,
Issue 23,
pp. 5854-5857
(2021)
•https://doi.org/10.1364/OL.438762

Self-calibrated BFP-type apertometer for both dry and immersion lenses via grating projection reference

Bei Zhang and Cuiling Zhang

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Bei Zhang and Cuiling Zhang, "Self-calibrated BFP-type apertometer for both dry and immersion lenses via grating projection reference," Opt. Lett. 46, 5854-5857 (2021)

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Abstract

This work proposes a novel scheme for a back focal plane (BFP)-type apertometer. The basic concept is to generate “multi-references” on BFP via the grating projection, which shows superiorities in two aspects: (1) a wider measurement range for both dry and immersion objectives; (2) higher accuracy via self-calibration of multi-references. To the best of our knowledge, this is the first approach and setup to allow the measurement of objectives with NA across unity via a “virtual” Fourier plane. It is also the first time to demonstrate a self-calibrated BFP-type apertometer with multi-references. All the involved concepts are experimentally verified.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Method		Measurement Range	Operation	Accuracy
Abbe apertometer [4]		$N A < 1$ or $N A > 1$ (different setups)	Simple	Medium (indistinct scale)
Geometric-based method [5]		$N A < 1$	Simple	Lower
BFP-type [2,6,7]	TIR	$N A > 1$	Not too complicated	Medium
BFP-type [2,6,7]	grating	One step and setup for both $N A > 1$ and $N A < 1$	Not too complicated	$\sqrt$ Higher with self-calibration $\sqrt$ Smaller division value

Notations	Explanations
$θ_{max}$	Maximum converging angle
$R_{C A}$	Radius of CA ring on BFP
$θ_{k}$	$k$ th diffraction angle
$x_{k}$	Projection location on BFP of $k$ th diffraction spot (distance between zeroth and $k$ th diffraction spots on BFP, $k = \pm 1, \pm 2 \dots$ )
$x_{k - c o r r e c}$	Distortion-corrected projection location on BFP of $k$ th diffraction spot (distance between zeroth and $k$ th diffraction spots on BFP, $k = \pm 1, \pm 2 \dots$ )
$N A_{k}$	Calculated NA by $k$ th diffraction spot, $k = \pm 1, \pm 2 \dots$
$N A_{k - c o r r e c}$	Distortion-corrected NA by $k$ th diffraction spot, $k = \pm 1, \pm 2 \dots$
NA	Final NA value by averaging ${N A}_{k}$

		Measured NA
Tested Lens	Labeled NA	Grating Reference	TIR Reference in [7]
Olympus, $10 \times$	0.25 (dry)	$0.252 \pm 0.001$	Inapplicable ( $\times$ )
Olympus, $20 \times$	0.40 (dry)	$0.404 \pm 0.002$	Inapplicable ( $\times$ )
Mitutoyo, $100 \times$	0.85 (dry)	$0.854 \pm 0.002$	Inapplicable ( $\times$ )
Olympus, $100 \times$	1.25 (oil)	$1.165 \pm 0.002$	$1.151 \pm 0.003$
Averaged	Abbe apertometer [4]		0.75%
error (%)	Geometry-based [5]		2.15%
	BFP-type	TIR reference [2,6,7]	0.30%
		Grating reference	0.23%

Method		Measurement Range	Operation	Accuracy
Abbe apertometer [4]		$N A < 1$ or $N A > 1$ (different setups)	Simple	Medium (indistinct scale)
Geometric-based method [5]		$N A < 1$	Simple	Lower
BFP-type [2,6,7]	TIR	$N A > 1$	Not too complicated	Medium
BFP-type [2,6,7]	grating	One step and setup for both $N A > 1$ and $N A < 1$	Not too complicated	$\sqrt$ Higher with self-calibration $\sqrt$ Smaller division value

Notations	Explanations
$θ_{max}$	Maximum converging angle
$R_{C A}$	Radius of CA ring on BFP
$θ_{k}$	$k$ th diffraction angle
$x_{k}$	Projection location on BFP of $k$ th diffraction spot (distance between zeroth and $k$ th diffraction spots on BFP, $k = \pm 1, \pm 2 \dots$ )
$x_{k - c o r r e c}$	Distortion-corrected projection location on BFP of $k$ th diffraction spot (distance between zeroth and $k$ th diffraction spots on BFP, $k = \pm 1, \pm 2 \dots$ )
$N A_{k}$	Calculated NA by $k$ th diffraction spot, $k = \pm 1, \pm 2 \dots$
$N A_{k - c o r r e c}$	Distortion-corrected NA by $k$ th diffraction spot, $k = \pm 1, \pm 2 \dots$
NA	Final NA value by averaging ${N A}_{k}$

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