# Measuring the Point Spread Function of a Fluorescence Microscope

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1 Frederick National Laboratory Measuring the Point Spread Function of a Fluorescence Microscope Stephen J Lockett, PhD Principal Scientist, Optical Microscopy and Analysis Laboratory Frederick National Laboratory National Cancer Institute

2 Contents Basics of image formation Why resolution is not perfect Theoretical spatial resolution limit Air versus immersion objective lenses Why it is important to measure Point Spread Function (PSF) How to measure PSF Examples of PSF measurements; why 3D is important Spherical aberration Objective Lenses and the Correction collar Confocal Fluorescence Microscopy

3 Basics of Image Formation depth 2D microscope image v 2 3D microscope image v 1 u 1 u 2 f Magnification, M = v u

4 Why resolution is not perfect: Wave Properties of Light Interference + = Constructive + = Destructive

5 Spatial Resolution in Optical Microscopy

6 The Optical Resolution Limit Spatial resolution, x = λ l d (Ernst Abbe, 1874) Numerical aperture, NA λ d 2l d and spatial resolution, x x = λ 2NN l

7 Theoretical Spatial Resolution Limit For conventional, fluorescence microscopy: λ em = 525 nm, NA = 1.4, n = Lateral resolution = 0.51 λ ee NN Depth resolution = 1.67 n λ ee NN 2 = 191 nm = 678 nm

8 Air Vs Immersion Objective Lenses objective For air, θ max = 41 o cover glass θ n air = 1.0, n oil = Image brightness = NA M 2

9 Why it is important to measure PSF 1) Know what level of detail to expect from the image. 2) Facilitates comparison of results acquired across different instruments. 3) Check that the microscope is performing optimally. The PSF checks the entire emission light path, not just the objective lens. 4) Know when it is better to use an oil or water objective lens. 5) Know when the correction collar is optimized. 6) Post-processing such as deconvolution require an accurate assessment of the PSF.

10 How to measure PSF 1) Prepare a sample of 0.1 µm diameter fluorescent beads dried onto a #1.5 coverslip (170 µm thick). Invert the coverslip onto a drop of high refractive index mounting medium (e.g. 15 µl of ProLong Gold for a 22 X 22 mm coverslip). Allow medium to cure. If the medium does not cure, then seal coverslip edges to the slide with nail enamel. 2) Instead of (1), pre-mounted bead slide can be purchased from Life Technologies (cat # T14792). 3) Clean the objective lens and bead slide. Ensure that the microscope is warmed up and stable. 4) Acquire a z stack of images with a depth spacing of at least one fifth of the expected axial resolution (for example a spacing of 120 nm for an oil, 1.4 NA lens). Also, ensure that the pixel size in the x / y directions is at least half the expected lateral resolution (for example 100 nm for an oil, 1.4 NA lens). 5) Generate an intensity profile in the z direction through the center of the bead and measure the full width half maximum (FWHM) of the profile. This is the axial resolution.

11 Examples of PSFs Y X Y Z Z X Intensity 100X, 1.49 NA Nikon lens, oil Depth Z X 10X, 0.3 NA Nikon lens, dry

12 Example of a Bad PSF Y X 100X, 1.3 NA lens, oil Z X

13 Spherical Aberration, Refractive Index Mismatch cell sample water y If n 1 = n 2 then all light rays from the lens will focus at a single point a distance y into the sample. n 1 (> n 2 ) oil n 2 θ 1 θ 2 x h When n 1 > n 2, the rays will bend downwards. Using Snell s law: sin θ 1 sin θ 2 = n 2 n 1 h 2 = ( n 2 n 1 ) 2 (x 2 + y 2 ) x 2 h is a function of x, Therefore rays crossing the interface from the oil to the cell at different distances (x) from the center will not focus at the same depth (h) in the cell. PreCongress Course

14 Using the Correct Immersion Media To avoid refractive index mismatch and the resulting spherical aberration, choose the right type of immersion objective. (Courtesy of ZOYC Live Cell Imaging Workshops 2010) PreCongress Course

15 Using the Correction Immersion Media Using water immersion objectives for samples in liquid media captures more signal and preserves resolution better than refractive index mismatched oil immersion objectives. oil immersion objective water immersion objective NA=1.4 NA=1.2 (Courtesy of ZOYC Live Cell Imaging Workshops 2010) PreCongress Course

16 Examples of Objective Lens PlanApo N model 60X magnification 1.40 Numerical aperture Oil Immersion media SC Super corrected Infinity corrected 0.17 Cover Glass thickness FN22 Field of view (0.22 mm) XL Plan N model 25X magnification 1.05 Numerical aperture W Water media MP Multi photon Infinity corrected Adjustable cover glass thickness FN18 Field of view (0.18 mm) PreCongress Course

17 Correct and Incorrect Correction Collar 100X, 1.49 lens, good collar 100X, 1.49 lens, bad collar PreCongress Course

18 PSF Equations for Confocal Microscopy For confocal fluorescence microscopy: Lateral resolution = 0.37 λ NA Axial resolution = 0.64 λ n n2 NA2, where λ = λexλem 2 λ 2 ex+λ 2 em PreCongress Course

19 Summary Understand conceptually why the spatial resolution of an optical microscope is not perfect. Merits of immersion lenses over dry lenses. Covered the basics of the procedure to measure the PSF. Recognize a good versus bad PSF Know the role of the correction collar. PreCongress Course

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