By

AJAL.A.J

MTF

Exposure Systems

Contact Proximity Projection

AJAL.A.J

Introduction: Historical and cultural relevance of MTS

Motivations: Why MTF supported also by incompetents (like me)

Technical issues: How do we achieve MTF and analyse its data (a few examples for MTF)

Scientific rationale: What can we do reasonably and first with MTF ?

SLIDES PREPARED FOR S8 ECE . METS SCHOOL OF ENGINEERING , MALA THRISSUR, KERALA , INDIA ON 10-12-09

modulation transfer function (MTF)

Instrument properties: (1) Linearity

• Linearity tested using high-quality test target

Set of squares of precisely calibrated optical absorbance

Note that the measured absorbance is greater than the real one.

This is due to the extra absorbing elements through which the beam passes between the reference and imaging detectors.

Measured absorbance

Re

al

ab

so

rba

nc

e

Line of unity

Instrument properties: (2) MTF

• MTF measured using alternating bands .

MTF limited by diameter of laser beam.

It is the beam size as it passes through the sample that matters:

Laser scanner design needs to be modified if resolution is to approach that of pixelated (CCD) scanners.

0.5 mm resolution

Instrument properties: (3) SNR

• Experimental test using different dye concentrations

Projection SNR defined by A / (A): direct measurement for squares on HQTT

Note that SNR 0 as A 0

Reconstruction SNR calculated via measurement of uniform dye in matching tank and then using data to simulate a scanned cylinder.

Peak SNR of almost 400 possibility of dose precision to < 0.5% !

Instrument properties: (4) Speed

• To date

Acquisition rate up to 65536 samples / s demonstrated.

Equivalent to a 256 × 256 projection image in 1 s.

Gives 2563 3-D image in 400 s 7 mins. At full Nyquist sampling

Images shown are acquired at around 20 mins. for a 2563 3-D image

This is comparable with the best performance of our CCD scanner

• The future ...

This architecture is very similar to that used in 3-D confocal microscopy.

In that field images are acquired at video frame rates.

We confidently expect 3-D scans in a minute or less.

DEFINE MTF ?

• The resolution and performance of an optical microscope can be characterized by a quantity known as the modulation transfer function (MTF), which is a measurement of the microscope's ability to transfer contrast from the specimen to the intermediate image plane at a specific resolution.

• Computation of the modulation transfer function is a mechanism that is often utilized by optical manufacturers to incorporate resolution and contrast data into a single specification.

• The modulation transfer function (MTF) indicates the ability of an optical system to reproduce (transfer) various levels of detail (spatial frequencies) from the object to the image.

• Its units are the ratio of image contrast over the object contrast as a function of spatial frequency.

• It is the optical contribution to the contrast sensitivity function (CSF).

MTF: Cutoff FrequencyMTF: Cutoff Frequency

0

0.5

1

0 50 100 150 200 250 300

1 mm2 mm4 mm6 mm8 mm

mo

du

lati

on

tra

nsf

er

spatial frequency (c/deg)

cut-off frequency

57.3cutoff

af

Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size

Another useful concept is the modulation transfer function or MTF, defined as shown below

MTF is the ratio between image intensity modulation over the object intensity modulation

This parameter qualifies the capability of an optical system

Photolithography- MTF

Function describes contrast as a function of size of features on the mask

Generally, MTF needs to be > 0.5 for the resist to resolve features

Photolithography- MTF

Modulation transfer function

i(x, y) o(x,y) PSF(x,y) noise

I(kx ,ky )O(kx , ky )MTF(kx ,ky ) noise

Information Processing by Human Observer

• Visual perception– Concerns how an image is perceived by a human

observer• preliminary processing by eye this lecture• further processing by brains

– Important for developing image fidelity measures• needed for design and evaluate DIP/DVP algorithms &

systems

imageimage eyeeye perceived imageperceived image

understanding of content

The Eye

– Cross section illustrationFigure is from slides at Gonzalez/ Woods DIP book website (Chapter 2)

Two Types of Photoreceptors at Retina

• Rods– Long and thin– Large quantity (~ 100 million)– Provide scotopic vision (i.e., dim light vision or at low illumination)– Only extract luminance information and provide a general overall

picture

• Cones– Short and thick, densely packed in fovea (center of retina)– Much fewer (~ 6.5 million) and less sensitive to light than rods– Provide photopic vision (i.e., bright light vision or at high illumination)

– Help resolve fine details as each cone is connected to its own nerve end– Responsible for color vision

our interest (well-lighted display)

Light

• Light is an electromagnetic wave– with wavelength of 350nm to 780nm stimulating human visual response

• Expressed as spectral energy distribution I()– The range of light intensity levels that human visual system can adapt is

huge: ~ on 10 orders of magnitude (1010) but not simultaneously

Luminance vs. Brightness

• Luminance (or intensity)– Independent of the luminance of surroundings

I(x,y,) -- spatial light distributionV() -- relative luminous efficiency func. of visual system ~ bell shape

(different for scotopic vs. photopic vision; highest for green wavelength, second for red, and least for blue )

• Brightness– Perceived luminance– Depends on surrounding luminance

Same lum. Different brightness

Different lum.

Similar brightness

Luminance vs. Brightness

• Example: visible digital watermark– How to make the watermark

appears the same gray levelall over the image?

Testing MethodologyTesting Methodology

Study Objective• To compare the image quality of different designs using

the modulation transfer function (MTF) testing method

Modulation Transfer Function (MTF) Testing• Objective method of measuring image contrast

degradation at different spatial frequencies

Study Objective• To compare the image quality of different designs using

the modulation transfer function (MTF) testing method

Modulation Transfer Function (MTF) Testing• Objective method of measuring image contrast

degradation at different spatial frequencies

The optical bench setup

Pinhole Target

IOL

Light Source

CCD Camera

MTF measurement systemMTF measurement system MTF measurement systemMTF measurement system

paradigmsparadigms

The IQ ReSTORThe IQ ReSTOR®® SN6AD3 aspheric SN6AD3 aspheric

intraocular lensintraocular lens (IOL) (IOL) produced the highest produced the highest overall image quality for MTFoverall image quality for MTF

Clinical investigation is needed to determine whether Clinical investigation is needed to determine whether superior IOL optical quality demonstrated in optical superior IOL optical quality demonstrated in optical bench testing results in measurable visual bench testing results in measurable visual improvements in clinical practiceimprovements in clinical practice

The IQ ReSTORThe IQ ReSTOR®® SN6AD3 aspheric SN6AD3 aspheric

intraocular lensintraocular lens (IOL) (IOL) produced the highest produced the highest overall image quality for MTFoverall image quality for MTF

Clinical investigation is needed to determine whether Clinical investigation is needed to determine whether superior IOL optical quality demonstrated in optical superior IOL optical quality demonstrated in optical bench testing results in measurable visual bench testing results in measurable visual improvements in clinical practiceimprovements in clinical practice

Image quality

• Spatial resolution can be best described by modulation transfer function (MTF)

• The limiting resolution of an imaging system is where the MTF approaches zero

• Higher magnification modes (smaller fields of view) are capable of better resolution

• Video imaging system degrades the MTF substantially

Color of LightColor of Light

Perceived color depends on spectral content (wavelength composition)

– e.g., 700nm ~ red.– “spectral color”

A light with very narrow bandwidth

A light with equal energy in all visible bands appears white

“Spectrum” from http://www.physics.sfasu.edu/astro/color.html

Perceptual Attributes of Color Perceptual Attributes of Color

Value of Brightness (perceived luminance)

Chrominance– Hue

specify color tone (redness, greenness, etc.)

depend on peak wavelength

– Saturation describe how pure the color is depend on the spread

(bandwidth) of light spectrum reflect how much white light is

added

RGB HSV Conversion ~ nonlinear

HSV circular cone is from online documentation of Matlab image processing toolbox

http://www.mathworks.com/access/helpdesk/help/toolbox/images/color10.shtml

• Any color can be reproduced by mixing an appropriate set of three primary colors

(Thomas Young, 1802)

Representation by Three Primary Colors

Example: Seeing Yellow Without Yellow

mix green and red light to obtain perception of yellow, without shining a single yellow photon

520nm 630nm570nm

=

Fourier Transform

The co-ordinate (ω) in Fourier space is often referred to as spatial frequency or just frequency

Graphical Representation Of The Fourier Transform

Convolution

Transfer Functions

• In Fourier Space this representation is simplified

)()()( sTsXsX inputoutput

0

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0.6

0.8

1

1.2

0 5 10 15 20 25

x =

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Point Spread Function (PSF)

• The blurring of an imaginary point as it passes through an optical system

• Convolution of the input function with a

0

0.2

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0.6

0.8

1

1.2

0 5 10 15 20 25 0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

dudvvuh

dudvvfufjvuh ff

YX

YX 2

2

),(

)](2exp[),(),(

H

By international agreement, the function is known as the optical transfer function (OTF) of the system and it is also the normalized autocorrelation of the amplitude transfer function.

Its modulus H is known as the modulation transfer function (MTF).

)(

)(PTFieMTFOTF

Where PTF is phase transfer function.

• MTF is the Fourier Transform Of the PSF

• MTF is a Transfer Function

CONCLUSION

)(

)(PTFieMTFOTF

Modulation Transfer Function (MTF)

• A representation of the point spread function in Fourier space

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

x =

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

0

0.5

1

1.5

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2.5

3

0 5 10 15 20 25

42

)},({)},({)},({

),(),(

),(),(),(

0

0

0

zySFzyIFZYIF

zySzyI

dydzzyIzZyYSZYI

i

i

),(exp),(

),()},({

ZYZY

ZY

kkikkM

kkTzySF

Transfer functions:

Optical transfer function T (OTF)

Modulation transfer function M (MTF)

Phase transfer function (PTF)

Frequency convolution theorem:

}{}{2

1}{ hFfFhfF

Example: Transform of a Gaussian wave packet.

akkxikax ekFeea

xE 4/)( 200

2

)( ,)(

Please prove it.

MTF Definition

• 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.

Imaging TaskAs 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.

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.

Good Poor

Contrast Modulation: A Basic MTF

Contrast Modulation is defined simply by averaging the difference of maximum and

minimum transmitted intensities:

“Spatial Frequency” typically implies an array of sine or bar targets at a given spacing, expressed in line-pairs-per-millimeter (lp/mm)

or cylces -per-milliradian (cy/mrad)

ContrastI I

I I

max min

max min

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

One line pair

Imax

Imin

Original Signal

Output Signal

Nyquist Sampling TheoryNyquist 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!)

Sample Intervals in Phase

Inpu

t Wav

efor

mS

ampl

ed O

utpu

t

Samples Out of Phase

Inpu

t Wav

efor

mS

ampl

ed O

utpu

t

Optical MTFImaging 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 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.

ImageObject

System MTFThe 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.

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.

Focal Plane Image Focal Plane Image

MTFsystem = MTFobjective*MTFdetector*MTFdisplay*MTFeyepiece*MTFeye

MTFsystem MTFLens1*MTFLens2

System MTFExample 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 mm cycles

mradkm( )

[2. ] [6 ]

tan[ / ]

4

1 104

Measurement: Knife EdgeKnife 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.

Edge Response

Line Spread

Differe-ntiate

Measurements of Image Quality

• PSF = Point Spread Function

• LSF = Line Spread Function

• CTF = Contrast Transfer Function

• MTF = Modulation Traffic Function

Point Spread FunctionPSF

• “Point” object imaged as circle due to blurring

• Causes– finite focal spot size– finite detector size– finite matrix size– Finite separation between object and detector

• Ideally zero

– Finite distance to focal spot• Ideally infinite

Quantifying Blurring• Object point becomes image circle

• Difficult to quantify total image circle size– difficult to identify beginning & end of object

Intensity

?

Quantifying BlurringFull Width at Half Maximum (FWHM)

• width of point spread function at half its maximum value

• Maximum value easy to identify

• Half maximum value easy to identify

• Easy to quantify width at half maximum

FWHM

Maximum

HalfMaximum

Line Spread FunctionLSF

• Line object image blurred

• Image width larger than object width

Intensity

?

Contrast Response FunctionCTF or CRF

• Measures contrast response of imaging system as function of spatial frequency

Lower

Frequency

Higher

Frequency

Loss of contrast between light and dark areas as bars & spaces get narrower. Bars & spaces blur into one another.

Contrast Response FunctionCTF or CRF

• Blurring causes loss of contrast– darks get lighter– lights get darker

Lower

Frequency

Higher

Frequency

Higher

Contrast

Lower

Contrast

Modulation Transfer FunctionMTF

• Fraction of contrast reproduced as a function of frequency

Recorded

Contrast(reduced by blur)

frequency

MTF

1

0

Contrast provided

to film

Freq. =

line pairs / cm

50%

MTF

• Can be derived from– point spread function– line spread function

• MTF = 1 means– all contrast reproduced at this frequency

• MTF = 0 means– no contrast reproduced at this frequency

MTF• If MTF = 1

– all contrast reproduced at this frequency

Recorded

Contrast

Contrast provided

to film

MTF• If MTF = 0.5

– half of contrast reproduced at this frequency

Recorded

Contrast

Contrast provided

to film

MTF• If MTF = 0

– no contrast reproduced at this frequency

Recorded

Contrast

Contrast provided

to film

Modulation Transfer Function (MTF)

MTF = Imax- Imin

Imax + Imin

-MTF is a measure of the contrast of an aerial pattern,

-For well-separated images,MTF ~ 1,

-For smaller images, MTF<1

-In general, MTF should be >0.5.

IntensityIntensity

DisplacementDisplacement

Component MTF• Each component in an imaging system has its own

MTF– each component retains a fraction of contrast as function

of frequency

• System MTF is product of MTF’s for each component.

• Since MTF is between 0 and 1,

• composite MTF <= MTF of poorest component

Modulation Transfer Function

• MTF is a measure of an imaging system’s ability to recreate the spatial frequency content of scene

MTF is the magnitude of the Fourier Transform ofthe Point Spread Function / LineSpread Function.

1.0

Cut-off

Spatial frequency

3 steps for MTF Measurement of IJ Printer

MTF of an IJ printer

1. Print a test target page 2. Scan the printed target

3. Analyze scanned data

Test Target Page

MTS : for noise reduction example

Low frequency noise artifacts are visible in the sky, which has been enhanced (darkened and boosted in contrast) for aesthetic purposes.

This is clear evidence of noise reduction– in a camera has an excellent reputation for low noise. The CMOS sensor evidently requires noise reduction.

MTF measurement methods: 1] Point source METHOD

Xe lamp: 3kW Xe lamp: 1kW

MTF measurement methods: step edge

Step edge method– Image of a target (artificial or natural) with a sharp transition between

dark and bright area– With a slight edge inclination, we can interleave successive rows (or

columns) to rebuild a sufficiently sampled response to Heaviside function

• Again, this is not necessary with THR mode

– Modulus of ratio of FT (edge response) to FT (edge) = in-flight MTF

Two kinds of edge– Natural edge: agricultural fields

• Difficulty to find a good one and to validate it

– Artificial edge• A checkerboard target has been laid out (Salon-de-Provence in south of France)• 60 x 60 m

Method Description• Edge Method (MTF estimation method)

– Sub-pixel edge locations were found by Fermi function fit.

– A least-square error line was calculated through the edge locations.

– Savitzky-Golay Helder-Choi filtering was applied on each line

– The filtered profile was differentiated to obtain LSF

– MTF calculated by applying Fourier transform to LSF.

Fig 1. Edge Method

• Pulse method– A pulse input is given to an imaging system.– Output of the system is the resulting image.– Edge detection and SGHC filtering was applied to get

output profile. – Take Fourier transform of the input and output.– MTF is calculated by dividing output by input.

Figure 2. Pulse method

10 12 14 16 18 20 22 24

2

4

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8

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12

14

Edge detection

Pix

els

Pixels

Curve inflection pointLeast square fit line

MTF measurement methods: Bi-resolution

Principle– Same landscape acquired with two spatial resolutions (same

spectral band)• High resolution image = reference• Low resolution image = sensor under assessment

– In-flight MTF = Modulus of ratio of FT (LR image) to FT (HR image)

Two situations– Satellite image versus aerial image

• Attempt with SPOT4 HRVIR

– Both sensors on the same satellite• Attempt with SPOT4: VGT1 versus HRVIR

MTF measurement methods: Periodic target

Opportunity to acquire Center radial target

THRESHOLD (5m) THRESHOLD (2.5m)

APPLICATIONSAPPLICATIONSThe MTF curves are used to characterize photographic The MTF curves are used to characterize photographic

objectives and are determined by the comparison of input objectives and are determined by the comparison of input images with their photographic reproductions. images with their photographic reproductions.

With this study the procedure is also extended to cases With this study the procedure is also extended to cases where the characterization of the acquisition system is not where the characterization of the acquisition system is not

possible.possible.

?ACQUISITION SYSTEM

OUTPUT IMAGE

INPUT IMAGE

?

MTF(f

f

ACQUISITION SYSTEM

OUTPUT IMAGE

INPUT IMAGE

MTF(f

f

AIM: AIM: extension of the traditional MTF technique to evaluate the extension of the traditional MTF technique to evaluate the debated resolution of the body image of the Turin Shroud. debated resolution of the body image of the Turin Shroud.

"“Relic certainly it is…”"“Relic certainly it is…” (John Paul II, April 28(John Paul II, April 28thth 1989) 1989)““The Shroud is provocation to the intelligence … The Shroud is provocation to the intelligence …

The Church submits to the scientists the assignment toThe Church submits to the scientists the assignment to keep on investigating”keep on investigating” (John Paul II, Turin 1998(John Paul II, Turin 1998

Purdue UniversityHP-Purdue Confidential 77

MTF (Modulation Transfer Function)MTF (Modulation Transfer Function)

• The MTF of an imaging system The MTF is the magnitude of the OTF (optical transfer function) as

.)0(

)()()(

H

fHfOTFfMTF

If the input signal x(·) is an impulse, then the MTF can be obtained by calculating |Y(f)| / |Y(0)|, where Y(f) is the impulse response of the system.

The MTF describes how much the system attenuates the input modulation signal as a function of frequency.

• MTF measurement by using a set of sinusoidal signals Measure the output response for a set of sinusoidal signals.

Extract the output magnitude at the given frequency for each sinusoidal signal.

Normalize the extracted output magnitudes and estimate the MTF curve.

Questions & Contacts

AJAL.A.J --- 4u.ajal@gmail.com

Phone: (9633 – 910 911)

www.ajal4u.0catch.com

http://www.metsengg.org/dept_home.php?dept_name=ece&opt=faculty

References• Modulation Transfer Function (MTF)

– Implement and compare different methods for calculating/measuring the MTF of an imaging lens

– Reference:• Backmann et al., “Random target method for fast MTF inspection,”

Optics Express, vol. 12, no. 12, pp. 2610 (2004)

• MTF with defocus– Implement and evaluate the MTF for a defocusing error– Reference:

• C. S. Williams, O.A. Becklund, “Introduction to the Optical Transfer Function,” (1989)

Thanks so much. It has been a pleasure.

Enjoy the meeting!

AJAL.AJ, ME .Assistant ProfessorMETS School of EngineeringUniversity of CalicutMala , Thrissur ( Dt )Email: 4u.ajal@gmail.com