Transcript Document
MTF Definition
Kyle R. Bryant
Tutorial Presentation: OPTI521 Distance
July 7, 2015
14:35:09
• MTF is a measure of
intensity contrast
transfer per unit
resolution of an image
or signal.
• It is used in optics,
electronics, and related
signal processing
applications.
jhimgrint
T
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DIFFRACTION MTF
13-Mar-00
DIFFRACTION LIMIT
0.0 FIELD ( 0.00 O)
0.7 FIELD ( -3.49 )O
1.0 FIELD ( -4.79 )O
-1.0 FIELD (
4.79 O)
WAVELENGTH WEIGHT
11500.0 NM
1
10000.0 NM
1
9000.0 NM
1
8000.0 NM
1
DEFOCUSING
1.0
0.00000
0.9
Focal Length 3.94"
0.8
F#/1.64
0.7
Pupil Diameter 2.4"
M
O 0.6
D
U
L 0.5
A
T
I
O 0.4
N
0.3
0.2
0.1
1.0
8.0
15.0
22.0
29.0
36.0
43.0
50.0
57.0
64.0
71.0
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SPATIAL FREQUENCY (CYCLES/MM)
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Imaging Task
Kyle R. Bryant
Tutorial Presentation: OPTI521 Distance
As spatial separation
decreases, the “good” system
maintains clear separation of
point source images, while the
“poor” system eventually can
no longer distinguish them.
MTF quantifies this
phenomenon in terms of
contrast between the center
peak intensities versus
intensity at their midpoint
across a scale of separation
distances.
Good
July 7, 2015
Poor
At large separations, even a poor system
can completely resolve the two images. As
separation decreases, only the good
systems can still recognize separate
sources.
2
Contrast Modulation: A Basic MTF
Tutorial Presentation: OPTI521 Distance
Kyle R. Bryant
July 7, 2015
1
Contrast Modulation is defined
simply by averaging the
difference of maximum and
minimum transmitted
0.9
Output
Signal
0.8
Imax
0.7
0.6
0.5
0.4
intensities:
Contrast
Imax Imin
Imax Imin
“Spatial Frequency” typically
implies an array of sine or bar
targets at a given spacing,
expressed in line-pairs-permillimeter (lp/mm) or cylces -
Imin
0.3
0.2
Original
Signal
0.1
0
0
200
400
600
800
1000
One line pair
per-milliradian (cy/mrad)
3
Nyquist Sampling Theory
Tutorial Presentation: OPTI521 Distance
Kyle R. Bryant
July 7, 2015
Input Waveform
Input Waveform
Nyquist Theory: In order to achieve perfect
reconstruction of an input signal which has a maximum
spatial frequency "f" (the cutoff), sampling must occur at
a rate of at least "2f". (Note: Phase is still an issue!)
Samples Out of Phase
Sampled Output
Sampled Output
Sample Intervals in Phase
4
Optical MTF
Kyle R. Bryant
Tutorial Presentation: OPTI521 Distance
Imaging optical systems perform
sampling, with the maximum
sample frequency determined by
the “spot size” image of a perfect
point source object (e.g., “Impulse
Response”).
A “perfect” optical system is limited
in resolution by wavelength (l)
dependent diffraction effects.
Lens aberrations can only worsen
performance.
The MTF of an optical system is
found by Fourier operations on the
“spot size”, or Point Spread
Function.
July 7, 2015
Image
Object
For an Object source at infinity distance:
F #
Focal Length
Pupil Diameter
For a Diffraction Limited Circular Aperture:
Diff . Ltd. Spot Radius 122
. l F#
MTF( )
2
( cos sin )
where lF #
MTF Cutoff Freq:
0
1
lp / mm
l F#
Frequency Scale Conversion:
10
. cy / mrad
1000
lp / mm
Focal Length ( mm)
5
System MTF
Kyle R. Bryant
Tutorial Presentation: OPTI521 Distance
The MTF of cascaded optical
assemblies is NOT equal to the
product of component MTF’s!
Why? Lenses transmit not just
intensity, but wavefront phase as
well, and hence aberrations in one
lens can cancel those in another.
July 7, 2015
Focal Plane Image
Focal Plane Image
MTFsystem MTFLens1*MTFLens2
MTF of cascaded objective
lenses, detector, and displays may
be multiplied for composite
“System MTF”, with a component
MTF measured at each intensity
transfer point.
MTFsystem = MTFobjective*MTFdetector*MTFdisplay*MTFeyepiece*MTFeye
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System MTF
Tutorial Presentation: OPTI521 Distance
Kyle R. Bryant
July 7, 2015
Example System MTF calculation:
Freq.
ObjLens
FPA
Display
Eyepiece
System
cy/mrad
MTF
MTF
MTF
MTF
MTF
1.0
0.9999
0.9999
0.9999
0.9999
0.99
2.0
0.90
0.99
0.99
0.90
0.79
3.0
0.85
0.98
0.92
0.88
0.67
For average human observers, MTF values around 0.05 are considered barely
resolvable. If the above system MTF reached 0.05 at 10 cy/mrad, for example, then
you can predict that a human observer could identify (6 cylce criteria) a 2.4 meter
taget through this sensor at a maximum range (this is a coarse estimate!) of about
Range ( m )
[2.4 m] [6 cycles]
4 km
tan[1 / 10 mrad ]
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Measurement: Mathematical Functions
Kyle R. Bryant
Tutorial Presentation: OPTI521 Distance
July 7, 2015
09:31:55
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2
1
1
1 2 2 2 1
1 1 3 1 1
1 25 52 25 1
3 52 100 52 3
1 25 52 25 1
1 1 3 1 1
1 2 2 2 1
1
1
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1
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1. Measure the instensity profile
("spot size") Point Spread
Function, or in 1D case, the Line
Spread Function, with an optical
instrument (not as easy as it
0.01412 mm
WAVELENGTH WEIGHT
555.0 NM
1
DIFFRACTION INTENSITY
SPREAD FUNCTION
POSITION 1
15-Mar-00
FLD( 0.00, 0.00)MAX;( 0.0, 0.0)DEG
DEFOCUSING: 0.000000 MM
sounds sometimes)
2. Calculate the modulus (absolute
value) of the Fourier Transform of
the PSF or LSF, cut out the
foldover reflection, normalize to
1.0, and set the frequency scale
based on cutoff calculation for n0
as shown earlier.
N 1
X ( k ) x( n)e
Discrete Fourier Transform:
2
j
nk
N
n0
A typical MTF plot is really
only one-dimensional (e.g.,
derived from the Line
Spread Function. Hence,
MTF's are typically plotted
with curves for orthogonal
Radial and Tangential
orientations.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
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Measurement: Knife Edge
Tutorial Presentation: OPTI521 Distance
Kyle R. Bryant
July 7, 2015
Knife Edge Measure of the Line
Spread Function (LSF):
1. Drag a knife-edge across the focal
plane of the optic to be tested and record
the intensity
2. Calculating the derivative of this data
gives us the LSF we are looking for so we
can continue with MTF.
3. The discrete derivative sequence di of a
sequence of numbers xi is easy:
Differentiate
di = ||xi - xi+1||
(we want the absolute values here)
Edge
Response
Line
Spread
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