Commonly used Equations
CAMERA RESOLUTION MAGNIFICATION
p
lp
ξ Camera mm
= 2 × H
ξCamera μm = 2 × s
SYSTEM RESOLUTION
m =
H
FOV
Calculating Field of View
ξSystem μm =
ξ Camera μm
m
lp
mm
lp
ξ = System m × ξCamera
mm
m =
AFOV = 2 × tan−1 2
f = (H × WD)
FOV
FOV = H × WD
Working Distance
How to Choose an Imaging Lens
f = Focal Length
m = Magnifi cation
FOV = Field of View
WD = Working Distance
NA = Numerical Aperture
f/# = F-Number
(f/#)w = Working f/#
ξ = Resolution
ØAiry Disk = Airy Disk Diameter
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
H
FOV
2f
f −1
Sensor Size (H)
Lens Selection, Small Sensors Lens Selection, Medium Format Sensors
Working Distance (mm)
500
400
300
200
100
0
1595
742.5
875
0 100 200 300 400 500 600 700 800 900 1000
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fixed focal
length lenses
large format lenses
lenses
variable
UV / IR / SWIR
magnification lenses
M12 / S-Mount
lenses
telecentric lenses
zoom lenses specialty lenses
imaging filters /
accessories
TECHNICAL NOTE
VARIABLE DEFINITIONS:
The fi gures below show Horizontal Field of View (FOV) vs. Working Distance
(WD) for four diff erent sensor sizes: (⅓ ", 1⁄1,8", ⅔ ", and 1"). By fi rst selecting
a sensor size and then fi nding the Horizontal FOV and WD required
on the plot, the appropriate focal length of the imaging lens that will work for
your application can be determined.
Important Considerations for Choosing an Imaging Lens:
• Longer focal length lenses have longer minimum working distances, which
is a consequence of their optical designs. Minimum working distance can
be shortened by adding spacers between the lens and camera, but image
quality will eventually suff er.
• Larger sensors provide larger FOVs with the same focal length lens. For
example, at a working distance of 350 mm, a 12 mm lens on a ⅔ " sensor
will have an FOV of about 370 mm, but on a 1" sensor at the same working
distance, the fi eld of view is approximately 530 mm - an increase of 43%.
• There are gaps in the plots, indicative that a standard off -the-shelf fi xed
focal length lens does not exist. For example, it is impossible to achieve
a 525 mm fi eld of view at a 600 mm working distance with a ⅔ " sensor
with available focal lengths. The closest lens that exists is an 8,5 mm focal
length, which would need to be used at a working distance of about 510
mm to achieve that fi eld of view.
*These plots are based on TECHSPEC® C Series Fixed Focal Length Lenses. However, these plots can be applied to any lens and are not limited to only the TECHSPEC® C Series Lenses.
1276
957
638
319
0
Horizontal FOV (mm, " Sensor)
Horizontal FOV (mm, 1" Sensor)
594
445.5
297
148.5
0
Horizontal FOV (mm, ." Sensor)
700
525
350
175
0
Horizontal FOV (mm, " Sensor)
0 100 200 300 400 500 600 700 800 900 1000
Working Distance (mm)
f=3.5mm
f=16mm
f=4.5mm
f=25mm
f=6mm
f=35mm
f=8.5mm
f=50mm
f=12mm
f=100mm
f=6mm
f=35mm
f=8.5mm
f=50mm
f=12mm
f=100mm
f=16mm f=25mm
AFOV
FOV
Object Plane
Image Plane
BFL
Entrance
Pupil
Exit
Pupil
Back Flange Distance
(17.526mm for C-Mount)
1" Ø-32 TPI
for C-Mount
FIXED FOCAL LENGTH LENSES
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