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Microscope 3D Point Spread Function Evaluation Method on a Confirmed applied sciences Article Microscope 3D Point Spread Function Evaluation Method on a Confirmed Object Plane Perpendicular to the Optical Axis Shuai Mao *, Zhenzhou Wang and Jinfeng Pan School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255000, China; [email protected] (Z.W.); [email protected] (J.P.) * Correspondence: [email protected] Received: 22 January 2020; Accepted: 1 April 2020; Published: 2 April 2020 Featured Application: A point spread function (PSF) evaluation method of a microscope on the object plane that is perpendicular to the optical axis is proposed. The proposed method can realize the 3D PSF on the perpendicular object plane, magnification, and paraxial region evaluation, and it can confirm any microscopic system. Abstract: A point spread function evaluation method for a microscope on the object plane that is perpendicular to the optical axis is proposed. The measurement of the incident beam direction from the dual position-sensitive-detector (PSD)-based units, the determination of the object plane perpendicularity and the paraxial region, and evaluation methods for the point spread function (PSF) are presented and integrated into the proposed method. The experimental verification demonstrates that the proposed method can achieve a 3D PSF on the perpendicular object plane, as well as magnification, paraxial region evaluation, and confirmation for any microscopic system. Keywords: point spread function; microscope; optical axis; object plane 1. Introduction In microscopic imaging, the imaging of a point-like light source does not appear as a point due to a diffraction pattern termed the point spread function (PSF). The PSF describes the analytical ability of the microscopic imaging of a point source and is a significant parameter for evaluating the resolution and quality of microscopic imaging systems. Therefore, an accurate measurement of the PSF is critical for the evaluation of microscopic systems [1,2]. The accurate measurement of the PSF is especially important when using super-resolution microscopic technologies [3,4]. For example, stochastic optical reconstruction microscopy and photo-activated localization microscopy both need accurate PSFs to fit each fluorescent point so that the center of each point can be exactly located [5–7]. Furthermore, structured illumination microscopy needs accurate PSFs to build the correct optical transfer function for image restoration and to obtain super-resolution images [8–11]. There are usually two ways to obtain a PSF: numerical calculations and experimental measurements. Numerical calculations require the PSF mode of lens theory because the difficult estimation of the pupil function often results in the theoretical model not reflecting the real imaging system [12,13]. Therefore, experimental measurements are the preferred method to obtain PSFs for microscopic systems. The most common methods for experimentally obtaining PSFs are the star point detection, knife-edge, and fluorescent microsphere detection methods [13,14]. The PSF for microscopic imaging is commonly obtained with the fluorescent microsphere detection method. The PSF should be measured on a pre-determined object plane that is perpendicular to the optical axis of the microscopic system (Figure1). The PSF has a correspondence relationship with an object Appl. Sci. 2020, 10, 2430; doi:10.3390/app10072430 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 2430 2 of 13 Appl. Sci. 2020, 1, x FOR PEER REVIEW 2 of 13 plane that is perpendicular to the optical axis, and a 3D PSF measurement is used to obtain each PSFeach on PSF its on corresponding its corresponding perpendicular perpendicular object planeobject at plane the focus at the depth. focus Realizing depth. R thisealizing goal this becomes goal morebecomes diffi morecult with difficult super-resolution with super-resolution microscopic microscopic measurements. measurements. A measured A measured object plane object that isplane not perpendicularthat is not perpendicular to the optical to axis the resultsoptical in axis an obtainedresults in PSF an thatobtained is not PSF homogeneous that is not duehomogeneous to a defocusing due etoff ecta defocusing along with effect the optical along axis with direction. the optical Moreover, axis direction. the accuracy Moreover, of the PSFthe isaccuracy significantly of the reduced PSF is whensignificantly the PSF reduced does not when have the a correspondingPSF does not have object a corresponding plane that is perpendicularobject plane that to is the perpendicular optical axis. Thisto the is opt especiallyical axis. important This is especially when the important PSF is employed when the in PSF 3D super-resolutionis employed in 3D microscopic super-resolution image restoration.microscopic Inimage this case,restoration. all the correspondingIn this case, all objectthe corresponding planes within object focal depthplanes mustwithin be focal confirmed. depth Twomust other be confirmed. microscopic T elementswo other are microscopic essential when elements obtaining are a PSF:essential the magnificationwhen obtaining and thea PSF: paraxial the region.magnification These elementsand the paraxial may change region. with These object elements plane variation may change along with the object optical plane axis. variation In summary, along if thethe measuredoptical axis. object In summary, plane that if is the perpendicular measured object to the plane optical that axis is perpendicular is not determined, to the the optical meanings axis ofis thenot PSF,determined, magnification, the meanings and paraxial of regionthe PSF, will magnification, be lost for super-resolution and paraxial microscopic region will measurements. be lost for Thesuper common-resolution methods microscopic for obtaining measurements. PSFs stated The above common are not methods able to determinefor obtaining the PSFs object stated planes above that are perpendicularnot able to determine to the optical the axis object or the planes longitudinal that are height perpendicular positions of to each the object optical plane axis along or the opticallongitudinal axis, asheight measuring positions these of factorseach object requires plane more along than the 3D optical PSF measurements. axis, as measuring these factors requires more than 3D PSF measurements. Image plane Ideal imaging region corresponding to the paraxial region of one perpendicularity object plane Optical system Microscope The measured Object plane Optical Axis Figure 1. The measured object plane is perpendicular to the optical axis of the microscopic system.system. InIn thisthis paper,paper, aa microscopemicroscope PSFPSF evaluationevaluation methodmethod forfor calibratingcalibrating the objectobject plane thatthat isis perpendicularperpendicular to thethe opticaloptical axisaxis isis proposed.proposed. The paraxialparaxial region,region, objectobject planeplane perpendicularityperpendicularity determination,determination, andand 3D3D PSF PSF evaluation evaluation methods methods are are presented. presented. The The presented presented methods, methods, together together with thewith integration the integration of dual-spot of dual position-spot detectionposition detection technology technology to realize ato 3D realize PSF on a the 3D perpendicular PSF on the objectperpendicular plane, facilitate object plane, the magnification facilitate the and magnification paraxial region and evaluation,paraxial region as well evaluation as the confirmation, as well as the of anyconfirmation microscopic of system.any microscopic The availability system. of the The proposed availabil methodity of is the then proposed experimentally method verified. is then experimentally verified. 2. Layout of PSF Measurement 2. LayoutThe proposed of PSF Measurement PSF measurement configuration consisted of a movable assembly (PSF calibration module)The andproposed a static assemblyPSF measurement (light source configuration and Z-axis position consist measuremented of a movable charge-coupled assembly devices (PSF (CCDs);calibration Figure module)2). The and core componenta static assembly was a dual (light position-sensitive-detector source and Z-axis position (PSD)-based measurement unit [ 15] thatcharge was-coupled within thedevices PSF calibration (CCD module.s); Figure The dual2). PSD-basedThe core unit wascomponent used to obtainwas thea incident dual beamposition direction-sensitive vector.-detector Here, (PSD) two PSDs-based were unit replaced [15] that by wa twos within CCDs th thate PSF could calibration obtain two module. light spots The fromdual twoPSD- dibasedfferent unit light wa routes.s used Into thisobtain way, the the incident dual PSD-based beam direction unit was vector. able toHere, obtain two two PSDs incident were beamreplaced light by direction two CCDs vectors that could at the obtain same two time. light When spots a light from beam two different reached onelight receiving routes. In plane, this way the, intensitythe dual PSD distribution-based unit of the wa lights able spot to obtain acted astwo a form incident of a Gaussianbeam light surface, direction and vectors the plane at the position same oftime. the When light spota light was beam directly reache obtainedd one byreceiving the PSD. plane The, intensitythe intensity distribution distribution of the of lightthe light spot spot was imagedacted as bya form the CCD, of a Gaussian and a Gaussian surface function, and the wasplane applied position to of fit the light intensity spot distribution;was directly then,obtained
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