Optimal lens design and use in laser-scanning microscopy

Abstract

In laser-scanning microscopy often an off-the-shelf achromatic doublet is used as a scan lens which can reduce the available diffraction-limited field-of-view (FOV) by a factor of 3 and introduce chromatic aberrations that are scan angle dependent. Here we present several simple lens designs of superior quality that fully make use of high-NA low-magnification objectives, offering diffraction-limited imaging over a large FOV and wavelength range. We constructed a two-photon laser-scanning microscope with optimized custom lenses which had a near diffraction limit point-spread-function (PSF) with less than 3.6% variation over a 400 µm FOV and less than 0.5 µm lateral color between 750 and 1050 nm.

Keywords: (180.0180) Microscopy; (180.1790) Confocal microscopy; (180.4315) Nonlinear microscopy; (220.3620) Lens system design; (220.3630) Lenses.

Fig. 1

Ideal layout of a 1D laser scanning microscope. Scanning is achieved by placing the scan mirror's rotation axis at the focal plane of the scan lens. The scan lens together with the tube lens form an afocal telescope system that projects an expanded image of the laser beam from the galvanometric mirror onto the objective pupil (or back-focal plane) that only pivots within the objective pupil without any lateral shift. As the focused spot moves across the sample, it generates fluorescence which is collected by the objective and in the case of two-photon laser scanning microscopy, directed on to one or more detectors by a dichroic mirror placed between the tube lens and objective.

Fig. 2

Optical aberrations for a 50 mm FL Thorlabs AC300-050-B achromat used as a scan lens for 3 mm (a) and 6 mm (b) gaussian beams (lens model in Appendix Table 1). (1) Optical layout and surface at which aberrations were studied. (2) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 250 mm FL (a) and 125 mm FL (b) tube lenses. (3) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (4) Lateral color taking the one-photon 1000 nm Airy disc as reference. (5) F-theta error. (6) Raytracing of lateral shift in the ideal Olympus XLPLN25xWMP objective pupil using 250 mm FL (a) and 125 mm FL (b) ideal tube lenses.

Fig. 3

Optical aberrations for 50 mm FL optimized achromats used as a scan lens for 3 mm (a) and 6 mm (b) gaussian beams (lens models in Appendix Table 2 and 3). (1) Optical layout and surface at which aberrations were studied. (2) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 250 mm FL (a) and 125 mm FL (b) tube lenses. (3) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (4) Lateral color taking the one-photon 1000 nm Airy disc as reference. (5) F-theta distortion. (6) Raytracing of lateral shift in the Olympus XLPLN25xWMP objective pupil using 250 mm FL (a) and 125 mm FL (b) ideal tube lenses.

Fig. 4

Optical aberrations for 50 mm FL Plössl-type scan lens assembled from two 100 mm FL Thorlabs AC300-100-B achromats used for 3 mm (a) and 6 mm (b) Gaussian beams (lens model in Appendix Table 4). (1) Optical layout and surface at which aberrations were studied. (2) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 250 mm FL (a) and 125 mm FL (b) tube lenses. (3) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (4) Lateral color taking the one-photon 1000 nm Airy disc as reference. (5) F-theta distortion. (6) Raytracing of lateral shift in the Olympus XLPLN25xWMP objective pupil using 250 mm FL (a) and 125 mm FL (b) ideal tube lenses.

Fig. 5

Optical aberrations for 50 mm FL optimized Plössl-type scan lens for 3 mm (a) and 6 mm (b) gaussian beams (lens models in Appendix Table 5 and 6). (1) Optical layout and surface at which aberrations were studied. (2) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 250 mm FL (a) and 125 mm FL (b) tube lenses. (3) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (4) Lateral color taking the one-photon 1000 nm Airy disc as reference. (5) F-theta distortion. (6) Raytracing of lateral shift in the Olympus XLPLN25xWMP objective pupil using 250 mm FL (a) and 125 mm FL (b) ideal tube lenses.

Fig. 6

Optical aberrations of a 4-element 50 mm FL 680-1600 nm optimized scan lens for a 3 mm gaussian beam (lens model inAppendix Table 7). (a) Optical layout and surface at which aberrations were studied. (b) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 250 mm FL tube lens. (c) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (d) Lateral color taking the one-photon 1000 nm Airy disc as reference. (e) F-theta distortion. (f) Raytracing of lateral shift in the Olympus XLPLN25xWMP objective pupil using a 250 mm FL ideal tube lens.

Fig. 7

Optical aberrations of a 4-element 50 mm FL 420-1600 nm optimized scan lens for a 4 mm gaussian beam (lens model in Appendix Table 8). (a) Optical layout and surface at which aberrations were studied. (b) Transmitted wavefront error. For reference, sample focus position is also shown (including f-theta error) using an ideal Olympus XLPLN25xWMP objective and ideal 190 mm FL tube lens. (c) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (d) Lateral color taking the one-photon 1000 nm Airy disc as reference. (e) F-theta distortion. (f) Raytracing of lateral shift in the Olympus XLPLN25xWMP objective pupil using a 190 mm FL ideal tube lens.

Fig. 8

Improved optical performance of a 250 mm FL custom-designed achromat used as a tube lens over a Thorlabs AC508-250-B with similar FL. (a, 1) Thorlabs AC508-250-B achromat (lens model in Appendix Table 9). (b, 1) Custom-designed achromat manufactured by Sill Optics Gmbh, Germany (lens model in Appendix Table 10) with 250 mm FL and used in the present two-photon laser-scanning microscope. (2) Transmitted wavefront error. For reference, sample focus position is also shown using an ideal Olympus XLPLN25xWMP objective. (3) Field curvature for the transversal (T) and sagittal (S) beam components, longitudinal color and astigmatism. (4) Lateral color taking the one-photon 1000 nm Airy disc as reference.

Fig. 9

Layout of our two-photon laser scanning microscope used to test the custom scan lens from (Fig. 6) and tube lens from (Fig. 8(b)). Two 90° off-axis parabolic mirrors PM were used as a 1:1 relay between the scan mirrors SM1 and SM2 to avoid lateral displacement of the beam during scanning within the objective BFP occurring with closely-spaced galvanometric mirrors. The scan lens SL and tube lens TL project an enlarged image of the initial beam from SM2 to the objective back-focal plane oBFP which passes through dichroic mirrors DM1 and DM2.

Fig. 10

Telecentric scan engine. (a) Two Newport 50329AU 90° off-axis parabolic mirrors with parent parabola focal length f of 25.4 mm form a 1:1 relay telescope between the two galvanometric mirrors. (b) Optical layout. (c) Scan engine assembly with scan mirrors SM1 and SM2 mounted in a cooling block and on precision translation stages, 90° off-axis parabolic mirrors PM and scan lens SL. (d) Diffraction-limited wavefront of an 850 nm 3 mm Ø beam passing through the scan engine assembly was measured after SM2 in the case when both mirrors were at 0° from the optical axis, and (e) at optical scan angles of SM1 between ± 14.3°. From the raw wavefront the following components were subtracted successively: tilt (blue), focus (green), 0° and 45° astigmatism (red), 0° and 90° coma (orange). Wavefront values are given as peak-to-valley (PV) in waves.

Fig. 11

High-resolution color-corrected imaging with constant PSF to within less than 3.6% width variation over more than 400 µm Ø FOV. (a) Calculated wavefront error in the objective pupil for the complete laser scanning microscope from (Fig. 9) using custom scan and tube lenses (Fig. 6 and Fig. 8(b)) over 680-1600 nm and 720 µm FOV when using the Olympus XLPLN25xWMP objective. (b) Calculated field curvature for sagittal (S) and transversal (T) beam components, longitudinal color and astigmatism at the sample location for the complete laser-scanning microscope assuming an ideal objective. (c) Calculated lateral color at sample location assuming an ideal objective. (d) Measured transversal and longitudinal two-photon excitation PSFs along the two orthogonal directions of the scan mirrors over the whole FOV (continuous lines) of the complete two-photon laser scanning microscope using the Olympus XLPLN25xWMP objective and comparison to theoretical value (dashed lines) of an aberration-free PSF. (e) Lateral and longitudinal chromatic PSF aberration of individual microspheres measured at 750 nm, 900 nm and 1050 nm.

Fig. 12

Monte Carlo tolerance analysis for lens production (100 runs). (a) 680-1600 nm custom-manufactured scan lens (Fig. 6 and Appendix Table 7). (b) 420-1600 nm lens model from (Fig. 7 and Appendix Table 8). (c) 680-1600 nm custom-manufactured tube lens from (Fig. 8(b) and Appendix Table 10).