Imaging Optics Reference Sheet
Calculating Field of View
m =
H
FOV
AFOV = 2 × tan−1 H
1
2 × s ξSensor= ξImage Space = × 1000 μm
ξObject Space = ξImage Space × m
ξObject Space μm =
ξ λ × (f/#) Diffraction Limit = × 1000 μm
f = Focal Length
m = Magnification
FOV = Field of View
WD = Working Distance
NA = Numerical Aperture
f/# = F-Number
(f/#)w = Working f/#
ξ = Resolution
ØAiry Disk = Airy Disk Diameter
Calculating f/# and NA
f/# =
f
ØEP
=
1
2 NA
Calculating Spacer Length
Variables Note: all variables assumed to be positive
θ = Marginal Ray Angle
I = Intensity
ØXP = Exit Pupil Diameter
α = Sensor Tilt
δ = Depth of Focus
D = Distortion
DTV = TV Distortion
λ = Wavelength
H = Sensor Size
AFOV = Angular Field of View
ØEP = Entrance Pupil Diameter
s = Pixel Size
d = Image Distance
p = Number of Pixels on a Sensor
Ø = Image Field Diameter
RI = Relative Illumination
Z = Axial Shift
n = Refractive Index
Imaging Equations
1 mm
Lens Mount
Last
Surface Image
s
m
f/# and working distance parameters for this MTF curve
10μm 5μm
Common Industrial Sensor Formats
www.edmundoptics.eu/eo-imaging
Lens
Manufacturer Focal
Length
Working
Distance Range
Thumbscrews
Minimum f/#
Part
Number
First
Surface
f/# Tick
Marks
Overall Length
Iris
Adjustment
Ring
Flange
Distance
Rear
Protrusion
Plane
Lens Shoulder
Focus
Adjustment
Ring
Filter
Thread
Focus 50mm
1.85 2 2.8 8 11
6mm/F1.85 #33-301
EDMUND OPTICS®
Lens Anatomy
2f
f = (H × WD)
FOV
(f/#)w ≈ (1 + m) × f/#
1
2 × (f/#) NAImage Space=
NAObject Space= n × sin(θ)
Minimum Spot Size = ØAiry Disk μm ≈ 2,44 × λ × (f/#)
1
1 mm
Calculating Resolution
1
d =
1
f
1
− WD
d
m = − WD
Spatial Frequency in Cycles Per mm
Pixel Size:
Contrast (%)
100
90
80
70
60
50
40
30
20
10
0
0.0 75.0
150.0
MTF: f/2.8, 218mm WD, #63-777
TS 5.50mm
TS 4.00mm
TS 0.00mm
Diff. Limit
Pixel limited resolution
by pixel size
(Nyquist Freq.)
15 - 20% contrast
is typically the
minimum contrast
for acceptable
image quality
Field Height
(multiply by 2 for
image circle diameter)
Lens Stock Number
Dashed Color Lines:
Tangential plane MTF
Solid Color Lines:
Sagittal plane MTF
MTF On-Axis
Diffraction Limit
Understanding MTF Curves
lp
mm
lp
mm
lp
mm
4.8 5.8 6.4 7.2
3.6 6.0 4.3 7.2 4.8 8.0 5.4 9.0
½ Inch
8.8
6.6 11.0
12.8
9.6 16
1 Inch
17.3
13 21.6
⁄ Inch
22.4
16.8 27.9
APS-C
29.2
20.2 35.5
APS-H
14.08
10.56 17.6
1.1 Inch
24
36
43.3
35mm
Inch ½.5 Inch ⁄.8 Inch Inch
/eo-imaging
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