F
reder
ick
N
at
ional
Labor
at
or
y
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
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
Basics of Image Formation
depth
2D microscope
image
3D microscope
image
u
2
f
v
2
u
1
v
1
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Magnification, M
=
v
Why resolution is not perfect:
Wave Properties of Light
Interference
+
=
Constructive
+
=
Destructive
Spatial Resolution in Optical Microscopy
The Optical Resolution Limit
x d l λSpatial resolution
, x =
𝜆 𝑙
𝑑
(
Ernst Abbe, 1874
)
Numerical aperture
, NA
≈
𝑑
2𝑙
and spatial resolution
,
x =
λ
Theoretical Spatial Resolution Limit
For conventional, fluorescence microscopy
:
Lateral resolution
=
0.51 ×
λ
𝑒𝑒𝑁𝑁
Depth resolution
=
1.67 × 𝑛 ×
λ
𝑒𝑒𝑁𝑁
2λ
em= 525 nm, NA = 1.4, n = 1.515
= 191 nm
= 678 nm
Air Vs Immersion Objective Lenses
n
air= 1.0, n
oil= 1.515
θ
For air
, θ
max= 41
oobjective
cover
glass
Image brightness
= NA
M
2
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.
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.
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Examples of PSFs
100X, 1.49 NA Nikon lens, oil X X Y Y Z Z Depth In te ns ity
10X, 0.3 NA Nikon lens, dry X
Example of a Bad PSF
100X, 1.3 NA lens, oil X Y X ZSpherical Aberration, Refractive Index Mismatch
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θ2 θ1 n2 n1 (> n2) x h y oil
cell sample ≈ water
•
If n
1= n
2then all light rays from
the lens will focus at a single
point a distance y into the
sample.
•
When n
1> n
2, the rays will bend
downwards.
•
Using Snell’s law:
sin θ1
sin θ2
=
n2
n1
•
h
2= (
n2
n1
)
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.
To avoid refractive index mismatch and the resulting spherical aberration,
choose the right type of immersion objective.
Using the Correct Immersion Media
oil immersion objective NA=1.4
water immersion objective NA=1.2
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.
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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
XL Plan N model 25X magnification 1.05 Numerical aperture W Water media MP Multi photon ∞ Infinity corrected
0 – 0.23 Adjustable cover glass thickness
Correct and Incorrect Correction Collar
100X, 1.49 lens, good collar
PSF Equations for Confocal Microscopy
For confocal fluorescence microscopy: Lateral resolution = 0.37 × λNA �
Axial resolution = 0.64 ×λ�
Summary
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