Abstract

Spatial light modulator (SLM) implementation of wavefront encoding enables various types of engineered point-spread functions (PSFs), including the generalized-cubic and squared-cubic phase mask wavefront encoded (WFE) PSFs, shown to reduce the impact of sample-induced spherical aberration in fluorescence microscopy. This investigation validates dynamic experimental parameter variation of these WFE-PSFs. We find that particular design parameter bounds exist, within which the divergence of computed and experimental WFE-PSFs is of the same order of magnitude as that of computed and experimental conventional PSFs, such that model-based approaches for solving the inverse imaging problem can be applied to a wide range of SLM-WFE systems. Interferometric measurements were obtained to evaluate the SLM implementation of the numeric mask. Agreement between experiment and theory in terms of a wrapped phase, 02π, validates the phase mask implementation and allows characterization of the SLM response. These measurements substantiate experimental practice of computational-optical microscope imaging with an SLM-engineered PSF.

© 2015 Optical Society of America

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References

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2015 (1)

N. Patwary and C. Preza, “Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions,” Biomed. Opt. Express Rev. 6, 3826–3841 (2015).

2014 (5)

N. Patwary, A. Doblas, S. V. King, and C. Preza, “Reducing depth induced spherical aberration by wavefront coding in 3D widefield fluorescence microscopy,” Proc. SPIE 8949, 894911 (2014).

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

2013 (2)

2012 (1)

2011 (2)

2010 (2)

G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. 48, 779–785 (2010).
[Crossref]

C. Preza and V. Myneni, “Quantitative depth-variant imaging for fluorescence microscopy using the COSMOS software package,” Proc. SPIE 7570, 757003 (2010).

2009 (1)

2008 (1)

2006 (2)

2004 (2)

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

C. Preza and J. A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[Crossref]

2003 (1)

J. Stockley and S. Serati, “Cascaded one-dimensional liquid crystal OPAs for 2-D beam steering,” Proc. IEEE 4, 1817–1822 (2003).

2002 (1)

1999 (1)

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999).
[Crossref]

1995 (1)

1992 (1)

S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 54–66 (1992).

1991 (1)

I. Csiszár, “Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems,” Ann. Statist. 19, 2032–2066 (1991).
[Crossref]

Arnison, M.

M. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.

Bernet, S.

Beversluis, M. R.

Bosch, S.

G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. 48, 779–785 (2010).
[Crossref]

Carles, G.

G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. 48, 779–785 (2010).
[Crossref]

Carnicer, A.

G. Carles, A. Carnicer, and S. Bosch, “Phase mask selection in wavefront coding systems: A design approach,” Opt. Lasers Eng. 48, 779–785 (2010).
[Crossref]

Cathey, W.

Cathey, W. T.

Chen, Y.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Cogswell, C. J.

M. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.

Conchello, J. A.

C. Preza and J. A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[Crossref]

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999).
[Crossref]

Cooper, J.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999).
[Crossref]

Csiszár, I.

I. Csiszár, “Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems,” Ann. Statist. 19, 2032–2066 (1991).
[Crossref]

Ding, H.

Doblas, A.

N. Patwary, A. Doblas, S. V. King, and C. Preza, “Reducing depth induced spherical aberration by wavefront coding in 3D widefield fluorescence microscopy,” Proc. SPIE 8949, 894911 (2014).

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

Dowski, E.

Dowski, E. R.

Engström, D.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20, 22334 (2012).
[Crossref]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3D Imaging (2012), paper DSu2C.3.

Escobar, I.

G. Saavedra, I. Escobar, R. Martínez-Cuenca, E. Sánchez-Ortiga, and M. Martnez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express 17, 13810–13818 (2009).
[Crossref]

I. Escobar, E. Sánchez-Ortiga, G. Saavedra, and M. Martínez-Corral, “New analytical tools for evaluation of spherical aberration in optical microscopy,” in Optical Fluorescence Microscopy (Springer, 2011), pp. 85–100.

Fürhapter, S.

Gibson, S. F.

S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 54–66 (1992).

Gillette, M. U.

Goksör, M.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20, 22334 (2012).
[Crossref]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3D Imaging (2012), paper DSu2C.3.

Hossain, M.

M. Hossain, S. V. King, and C. Preza, “Enhanced extended depth-of-field microscopy via modeling of SLM effects on the applied phase mask,” in Imaging and Applied Optics, OSA Technical Digest (2014), paper IW4C.4.

Jesacher, A.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Karpova, T.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999).
[Crossref]

King, S. V.

N. Patwary, A. Doblas, S. V. King, and C. Preza, “Reducing depth induced spherical aberration by wavefront coding in 3D widefield fluorescence microscopy,” Proc. SPIE 8949, 894911 (2014).

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

M. Hossain, S. V. King, and C. Preza, “Enhanced extended depth-of-field microscopy via modeling of SLM effects on the applied phase mask,” in Imaging and Applied Optics, OSA Technical Digest (2014), paper IW4C.4.

Lanni, F.

S. F. Gibson and F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 9, 54–66 (1992).

Martinez-Corral, M.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

Martínez-Corral, M.

I. Escobar, E. Sánchez-Ortiga, G. Saavedra, and M. Martínez-Corral, “New analytical tools for evaluation of spherical aberration in optical microscopy,” in Optical Fluorescence Microscopy (Springer, 2011), pp. 85–100.

Martínez-Cuenca, R.

Martnez-Corral, M.

Maurer, C.

McNally, J. G.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, “Three-dimensional imaging by deconvolution microscopy,” Methods 19, 373–385 (1999).
[Crossref]

Millet, L.

Mir, M.

Myneni, V.

C. Preza and V. Myneni, “Quantitative depth-variant imaging for fluorescence microscopy using the COSMOS software package,” Proc. SPIE 7570, 757003 (2010).

Novotny, L.

Patwary, N.

N. Patwary and C. Preza, “Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions,” Biomed. Opt. Express Rev. 6, 3826–3841 (2015).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

N. Patwary, A. Doblas, S. V. King, and C. Preza, “Reducing depth induced spherical aberration by wavefront coding in 3D widefield fluorescence microscopy,” Proc. SPIE 8949, 894911 (2014).

Pauca, V.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

Pavani, S. R. P.

Persson, M.

M. Persson, D. Engström, and M. Goksör, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20, 22334 (2012).
[Crossref]

D. Engström, M. Persson, and M. Goksör, “Spatial phase calibration used to improve holographic optical trapping,” in Biomedical Optics and 3D Imaging (2012), paper DSu2C.3.

Peterka, D. S.

Piestun, R.

Plemmons, R.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

Popescu, G.

Prasad, S.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

Preza, C.

N. Patwary and C. Preza, “Image restoration for three-dimensional fluorescence microscopy using an orthonormal basis for efficient representation of depth-variant point-spread functions,” Biomed. Opt. Express Rev. 6, 3826–3841 (2015).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

N. Patwary, A. Doblas, S. V. King, and C. Preza, “Reducing depth induced spherical aberration by wavefront coding in 3D widefield fluorescence microscopy,” Proc. SPIE 8949, 894911 (2014).

S. Yuan and C. Preza, “Point-spread function engineering to reduce the impact of spherical aberration on 3D computational fluorescence microscopy imaging,” Opt. Express 19, 23298–23314 (2011).
[Crossref]

C. Preza and V. Myneni, “Quantitative depth-variant imaging for fluorescence microscopy using the COSMOS software package,” Proc. SPIE 7570, 757003 (2010).

C. Preza and J. A. Conchello, “Depth-variant maximum-likelihood restoration for three-dimensional fluorescence microscopy,” J. Opt. Soc. Am. A 21, 1593–1601 (2004).
[Crossref]

M. Hossain, S. V. King, and C. Preza, “Enhanced extended depth-of-field microscopy via modeling of SLM effects on the applied phase mask,” in Imaging and Applied Optics, OSA Technical Digest (2014), paper IW4C.4.

Quirin, S.

Ritsch-Marte, M.

Rogers, J.

Saavedra, G.

A. Doblas, S. V. King, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Investigation of the SQUBIC phase mask design for depth-invariant widefield microscopy point-spread function engineering,” Proc. SPIE 8949, 894914 (2014).

S. V. King, A. Doblas, N. Patwary, G. Saavedra, M. Martinez-Corral, and C. Preza, “Implementation of PSF engineering in high-resolution 3D microscopy imaging with a LCoS (reflective) SLM,” Proc. SPIE 8949, 894913 (2014).

G. Saavedra, I. Escobar, R. Martínez-Cuenca, E. Sánchez-Ortiga, and M. Martnez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express 17, 13810–13818 (2009).
[Crossref]

I. Escobar, E. Sánchez-Ortiga, G. Saavedra, and M. Martínez-Corral, “New analytical tools for evaluation of spherical aberration in optical microscopy,” in Optical Fluorescence Microscopy (Springer, 2011), pp. 85–100.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Sánchez-Ortiga, E.

G. Saavedra, I. Escobar, R. Martínez-Cuenca, E. Sánchez-Ortiga, and M. Martnez-Corral, “Reduction of spherical-aberration impact in microscopy by wavefront coding,” Opt. Express 17, 13810–13818 (2009).
[Crossref]

I. Escobar, E. Sánchez-Ortiga, G. Saavedra, and M. Martínez-Corral, “New analytical tools for evaluation of spherical aberration in optical microscopy,” in Optical Fluorescence Microscopy (Springer, 2011), pp. 85–100.

Serati, S.

J. Stockley and S. Serati, “Cascaded one-dimensional liquid crystal OPAs for 2-D beam steering,” Proc. IEEE 4, 1817–1822 (2003).

Sheppard, C. J. R.

M. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.

Stockley, J.

J. Stockley and S. Serati, “Cascaded one-dimensional liquid crystal OPAs for 2-D beam steering,” Proc. IEEE 4, 1817–1822 (2003).

Stranick, S. J.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Torgersen, T.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

Török, P.

M. Arnison, C. J. Cogswell, C. J. R. Sheppard, and P. Török, “Wavefront coding fluorescence microscopy using high aperture lenses,” in Optical Imaging and Microscopy: Techniques and Advanced Systems, P. Török and F.-J. Kao, eds. (Springer, 2003), pp. 143–165.

Unarunotai, S.

van der Gracht, J.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. van der Gracht, “High-resolution imaging using integrated optical systems,” Int. J. Imaging Syst. Technol. 14, 67–74 (2004).
[Crossref]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photonics 8, 302–306 (2014).
[Crossref]

Wang, Z.

Wu, S. T.

S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

Xie, X.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Yang, D. K.

S. T. Wu and D. K. Yang, Fundamentals of Liquid Crystal Devices (Wiley, 2006).

Yang, K.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).

Yuan, S.

Yuste, R.

Zhou, J.

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Figures (6)

Fig. 1.
Fig. 1.

Effect of SLM relay on image frequency spectrum. (a) XY and XZ sections of measured PSFs for the top and side imaging ports from images of fluorescent emission (608 nm) emitted by 0.175 μm beads obtained with a 63 × / 1.4 NA oil-immersion objective lens. (b) XY and XZ sections of the 3D MTF computed from the measured PSF. An arrow indicates the theoretical cut-off frequency. (c) Vertical profiles through the MTF along f x for f y = f z = 0 . The SLM-WFE imaging path does not contribute significant aberrations to the image.

Fig. 2.
Fig. 2.

Configuration for experimental and simulated measurement of the SLM-implemented phase mask. (a) Experimental Mach–Zehnder schematic. Off-axis illumination on the SLM replicates configuration used in the microscope WFE imaging path. Collimating lens, L c ; f c = 100 mm ; imaging lenses, L 1 and L 2 ; f 1 = 100 mm , f 2 = 50 mm ; M, mirror; BS, beam splitter; the CCD is a Zeiss Axiocam MRm. (b) Loss in transmitted amplitude occurs at locations of 0 2 π wrapped phase, evident in the brightfield image acquired from the SLM in the case of the GCPM, due to extreme changes in LC molecular orientation between adjacent pixels. The simulated image demonstrates how this loss is accounted for in phase mask comparison. (c) Effect of the SLM in the off-axis configuration is accounted for in simulation by a numeric phase mask convolved with the SLM response shown here as the SLM-modified mask in the case of the CPM.

Fig. 3.
Fig. 3.

Verification of wavefront phase implemented with a LC-SLM. Computed phase mask designs are compared with their SLM implementation using experimental and simulated interferometry: (a) CPM, α = 30 ; (b) GCPM, α = 50 , β = 50 ; (c) SQUBIC, A = 50 . Measured, simulated, and computed wrapped phase images are displayed on a minimum to maximum gray scale. Profiles, plotted to the right of the corresponding phase images, are aligned at their center point and are taken along: a diagonal direction (top right to bottom left) in the case of the CPM image; the horizontal direction in the case of GCPM; and the vertical direction in the case of the SQUBIC mask. Experimental measurement shows the average and variance (red error bars) of 12 realizations of wavefront encoding SLM phase mask modulation. The number of 0 2 π wrapped phase lines in the measured, simulated, and computed cases agrees for all phase masks with some error in the pattern spatial fidelity and reduced modulation depth.

Fig. 4.
Fig. 4.

Effect of reduced SLM modulation depth on the WFE-PSF due to a high density of wrapped phase lines per pixel is demonstrated on experimental CPM WFE-PSFs with varying values of the α design parameter. In the top row, CPM phase masks for different α are shown for each case (wrapped on the left and unwrapped on the right). XY section images and XZ section images are shown, respectively, in the middle and bottom row for different design parameter values: (a,b) α = 20 ; (c,d) α = 30 ; (e,f) α = 50 ; (g,h) α = 70 ; and (i,j) α = 100 . Lens, 63 × , 1.4 NA; wavelength, 515 nm. Δ n = 0.05 between coverslip and mounting medium, point source is located at 25 μm depth below the coverslip. The SLM can implement a limited number of wrapped phases ( 0 2 π ), i.e., a limited maximum phase delay, depending on the aperture size, pixel size, and cross-talk effects.

Fig. 5.
Fig. 5.

3D WFE-PSF intensities (used for quantitative comparison, Table 1) show good agreement between experiment and simulation at 25 μm below the coverslip when the response of the SLM is simulated. Comparison of experiment with simulation of a point source at both 0 μm (ideal conditions) and 25 μm depths below the coverslip highlights the effect of SA on the designed properties of the WFE-PSFs using the (a) GCPM and the (b) SQUBIC phase mask. In each case, the lateral (XY) view (top row) is shown at the best focus axial location, while corresponding axial (XZ) view (bottom row) is shown for y = 0 . Experimental images are displayed using different intensity scales and are saturated to show low-intensity details of the diffracted signal. Simulated and experimental PSFs are computed and acquired with a 63 × , 1.4 NA oil-immersion lens and a 515 nm wavelength.

Fig. 6.
Fig. 6.

Effect of change in sign of SA and varying design parameter A in the SQUBIC phase mask design. XY section images (top row) and XZ section images (bottom row) from the center of the SQUBIC-PSFs. A lower A value reduces the number of 0 2 π wrapped phase cycles in the SQUBIC phase mask (top row) and decreases the PSF’s axial extent compared to the PSFs in Fig. 5(b). PSFs are computed and measured with SA, which is opposite in sign to the aberration in PSFs shown in Fig. 5. This sign change is induced by a change in mounting medium (i.e., by a change in the RI difference), but qualitative agreement, between measured and computed PSFs, remains. Experimental images are displayed using different intensity scales and are saturated to show low-intensity details of the diffracted signal. Lens: 63 × . Wavelength: 515 nm.

Tables (1)

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Table 1. Comparison of Experimental and Simulated PSFs

Equations (3)

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φ GCPM ( f x , f y ) = α ( f x 3 + f y 3 ) + β ( f x 2 f y + f x f y 2 ) .
ϕ SQUBIC ( f x , f y ) = A ( 1 ( f x 2 + f y 2 ) sin 2 α m 1 1 cos α m + 0.5 ) 3 ,
ϕ ( x , y ) = cos 1 ( I ( x , y ) I ref ( x , y ) I sple ( x , y ) 2 I ref ( x , y ) I sple ( x , y ) ) ,

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