Abstract
We constructed a new concentric black and white (B/W) hexagonal aperture, and we resized the image in a matrix of dimensions 1024 × 1024 pixels using MATLAB code. We derived a new formula for the point spread function (PSF) corresponding to the B/W hexagonal aperture. We computed the PSF using the Fast Fourier transform and compared the results with the case of a transparent hexagonal shape. In addition, we computed the coherent transfer function (CTF) for two symmetric objectives provided with the B/W hexagonal aperture. Finally, we reconstructed the image from the input object located in the confocal plane of the microscope provided with the modulated hexagonal apertures. We showed that the full width of the central lobe is smaller than that corresponding to the transparent hexagonal aperture hence improved resolution is attained in the case of B/W hexagonal aperture. In addition, we showed significant Legs of diffraction pattern corresponding to the B/W concentric hexagonal aperture. Then the PSF is dependent on the geometry of the B/W hexagonal aperture. We conclude that the image resolution which depends on the PSF is improved in the case of B/W hexagonal aperture while the image contrast is affected by the transmitted intensity in the detection plane of the confocal microscope. The coherent transfer function (CTF) or the autocorrelation corresponding to the B/W concentric hexagonal aperture has triangular decaying fringing as compared to that corresponding to the uniform hexagonal and circular apertures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
No data associated with the manuscript.
Abbreviations
- PSF:
-
Point spread function
- FFT:
-
Fast Fourier transforms
- CTF:
-
Coherent transfer function
- CSLM:
-
Confocal scanning laser microscope
- FWHM:
-
Full width at half maximum
- B/W:
-
Black and white
References
Chen, N., Wong, C.H., Sheppard, C.J.R.: Focal modulation microscopy. Opt. Express. 16(23), 18764–18769 (2008)
Clair, J.J., Hamed, A.M.: Theoretical studies on the optical coherent microscope. Optik. 64, 133–141 (1983)
Deng, A., Zheng, Y., et al.: Improved spatial resolution using focal modulation microscopy with a Tai Chi aperture. Opt. Express. 29(12), 18263–18276 (2021). https://doi.org/10.1364/OE.426600
Gong, W., Si, K., Chen, N., Sheppard, C.J.R.: Improved spatial resolution in fluorescence focal modulation microscopy. Opt. Lett. 34(22), 3508–3510 (2009). https://doi.org/10.1364/OL.34.003508
Goodman, J.W.: Introduction to Fourier Optics. Roberts and Company Publishers, Englewood (2005)
Hamed, A.M.: Numerical speckle images formed by diffusers using modulated conical and linear apertures. J. Mod. Opt. 56(10), 1174–1181 (2009a). https://doi.org/10.1080/09500340902985379
Hamed, A.M.: Formation of speckle images formed for diffusers illuminated by modulated apertures (circular obstruction). J. Mod. Opt. 56, 1633–1642 (2009b). https://doi.org/10.1080/09500340903277792
Hamed, A.M.: Discrimination between speckle images using diffusers modulated by some deformed apertures: Simulations. J. Opt. Eng. 50(1), 018202–018202 (2011). https://doi.org/10.1117/1.3530085
Hamed, A.M.: Study of graded index and truncated apertures using speckle images. Precis. Instrum. Mech. PIM 3, 144–152 (2014)
Hamed, A.M.: Improvement of point spread function (PSF) using linear- quadratic aperture. Optik. 131, 838–849 (2017). https://doi.org/10.1016/2016.11.201
Hamed, A.M.: Application of a hexagonal aperture on the confocal scanning laser microscope. Opt. Quant. Electron. 55, 749 (2023). https://doi.org/10.1007/s11082-023-04920-8
Hamed, A.M., Clair, J.J.: Studies on optical properties of confocal scanning optical microscope using pupils with radially transmission distribution. Optik. 65, 209–218 (1983a)
Hamed, A.M., Clair, J.J.: Image, and super-resolution in optical coherent microscopes. Optik. 64, 277–284 (1983b)
HeintZman, R., Huser, T.: Super-resolution structured illumination microscopy. Chem. Rev. 117, 23, 13890–13908 (2017). https://doi.org/10.1021/acs.chemrev.7b00218
Itoh, S., Matsuo, T., et al.: Point spread function of hexagonally segmented telescopes by new symmetrical formulation. MNRAS. 483, 119–131 (2019)
Krishnendu, S., Joby, J.: An overview of structured illumination microscopy: recent advances and perspectives. J. Opt. 23, 123002 (2021). https://doi.org/10.1088/2040-8986/ac3675
Mohamed, A.M., Mohsen, S.H., et al.: A hexagonal aperture to reduce spherical aberration. Neuro Quantol 20(6), 2599–2602 (2022)
Sabatke, E., Burge, J., et al.: Analytic diffraction analysis of a 32-m telescope with hexagonal segments for high-contrast imaging. Appl. Opt. 44(8), 1360–1365 (2005)
Sheppard, C.J.R.: The development of microscopy for super-resolution. Appl. Sci. 11, 8981 (2021). https://doi.org/10.3390/11198981
Si, K., Gong, W., Chen, N., Sheppard, C.J.R.: Enhanced background rejection in thick tissue using focal modulation microscopy with quadrant apertures. Opt. Commun. 284(5), 1475–1480 (2011)
Xu, Q.J., Ma, H.A., et al.: Stochastic optical reconstruction microscopy. Curr Protoc. Cytom 81, 12–46 (2017). https://doi.org/10.1002/cpcy.23
Wu, C., Zheng, Y., et al.: Improvements with divided cosine-shaped apertures in confocal microscopy. Opt. Commun. 442, 71–76 (2019)
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
I studied a modulated hexagonal aperture formed of concentric black and white hexagons. Then, I calculated the point spread function (PSF) or the amplitude impulse response corresponding to the modulated hexagonal aperture. The resolution is improved in the case of B/W hexagonal aperture compared to that corresponding to the transparent hexagonal and circular apertures. In addition, I showed interest in the black and white (B/W) hexagonal pupil over the uniform hexagonal with stringent secondary legs. Hence, this type of modulated aperture is considered helpful for imaging extended objects. We get the reconstructed image of the coronary arteries using the confocal scanning laser microscope (CSLM) provided with the two objectives of the microscope with B/W hexagonal apertures.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no competing interests.
Ethical approval
Not applicable.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hamed, A.M. Investigation of a concentric black and white hexagonal pupil and its application in confocal microscopic imaging. Opt Quant Electron 55, 1279 (2023). https://doi.org/10.1007/s11082-023-05563-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-023-05563-5