modulation transfer function (MTF)

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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.

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  • Photoreceptors – also called light receptor (receptor is sense organ that is a cell or groups of cells that receives stimuli)
    Color objects often appear as colorless in dim light because only the rods are stimulated.
  • If the mix of green and red light trigger the same sensation of the R/G/B cones as the yellow light does, we will see the mix as yellow.
  • modulation transfer function (MTF)

    1. 1. By AJAL.A.J MTF
    2. 2. Exposure Systems Contact Proximity Projection
    3. 3. 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)
    4. 4. 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 Realabsorbance Line of unity
    5. 5. 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
    6. 6. Instrument properties: (3) SNR • Experimental test using different dye concentrations Projection SNR defined by A / σ(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% !
    7. 7. 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.
    8. 8. 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.
    9. 9. • 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).
    10. 10. MTF: Cutoff FrequencyMTF: Cutoff Frequency 0 0.5 1 0 50 100 150 200 250 300 1 mm 2 mm 4 mm 6 mm 8 mm modulationtransfer spatial frequency (c/deg) cut-off frequency 57.3 cutoff a f λ = ⋅ Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size
    11. 11. 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
    12. 12. 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
    13. 13. Modulation transfer function i(x,y)=o(x,y)⊗PSF(x,y) +noise c c c c I(kx,ky)=O(kx,ky)⋅MTF(kx,ky)+ℑnoise{ }
    14. 14. 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
    15. 15. The Eye – Cross section illustration Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 2)
    16. 16. 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)
    17. 17. Light • Light is an electromagnetic wave – with wavelength of 350nm to 780nm stimulating human visual response • Expressed as spectral energy distribution I(λ) – The range of light intensity levels that human visual system can adapt is huge: ~ on 10 orders of magnitude (1010 ) but not simultaneously
    18. 18. Luminance vs. Brightness • Luminance (or intensity) – Independent of the luminance of surroundings I(x,y,λ) -- spatial light distribution V(λ) -- 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
    19. 19. Luminance vs. Brightness • Example: visible digital watermark – How to make the watermark appears the same gray level all over the image?
    20. 20. 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
    21. 21. The optical bench setup Pinhole Target IOL Light Source CCD Camera MTF measurement systemMTF measurement systemMTF measurement systemMTF measurement system
    22. 22. paradigmsparadigms  The IQ ReSTORThe IQ ReSTOR®® SN6AD3 asphericSN6AD3 aspheric intraocular lensintraocular lens (IOL)(IOL) produced the highestproduced the highest overall image quality for MTFoverall image quality for MTF  Clinical investigation is needed to determine whetherClinical investigation is needed to determine whether superior IOL optical quality demonstrated in opticalsuperior IOL optical quality demonstrated in optical bench testing results in measurable visualbench testing results in measurable visual improvements in clinical practiceimprovements in clinical practice  The IQ ReSTORThe IQ ReSTOR®® SN6AD3 asphericSN6AD3 aspheric intraocular lensintraocular lens (IOL)(IOL) produced the highestproduced the highest overall image quality for MTFoverall image quality for MTF  Clinical investigation is needed to determine whetherClinical investigation is needed to determine whether superior IOL optical quality demonstrated in opticalsuperior IOL optical quality demonstrated in optical bench testing results in measurable visualbench testing results in measurable visual improvements in clinical practiceimprovements in clinical practice
    23. 23. 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
    24. 24. 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
    25. 25. Perceptual Attributes of ColorPerceptual 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/acc ess/helpdesk/help/toolbox/imag es/color10.shtml
    26. 26. • Any color can be reproduced by mixing an appropriate set of three primary colors (Thomas Young, 1802) Representation by Three Primary Colors
    27. 27. Example: Seeing Yellow Without Yellow mix green and red light to obtain perception of yellow, without shining a single yellow photon 520nm 630nm 570nm =
    28. 28. Fourier Transform The co-ordinate (ω) in Fourier space is often referred to as spatial frequency or just frequency
    29. 29. Graphical Representation Of The Fourier Transform
    30. 30. Convolution
    31. 31. Transfer Functions • In Fourier Space this representation is simplified )()()( sTsXsX inputoutput ⋅= 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 2 2.5 3 0 5 10 15 20 25
    32. 32. 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 0.4 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
    33. 33. ∫ ∫ ∫ ∫ ∞ ∞− ∞ ∞− +− = dudvvuh dudvvfufjvuh ff YX YX 2 2 ),( )](2exp[),( ),( π 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). )( )( PTFi e MTFOTF = Where PTF is phase transfer function.
    34. 34. • MTF is the Fourier Transform Of the PSF • MTF is a Transfer Function CONCLUSION )( )( PTFi e MTFOTF =
    35. 35. 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 2 2.5 3 0 5 10 15 20 25
    36. 36. 42 )},({)},({)},({ ),(),( ),(),(),( 0 0 0 zySFzyIFZYIF zySzyI dydzzyIzZyYSZYI i i ⋅= ⊗= −−= ∫ ∫ +∞ ∞− +∞ ∞− [ ]),(exp),( ),()},({ ZYZY ZY kkikkM kkTzySF Φ= = Transfer functions: Optical transfer function T (OTF) Modulation transfer function M (MTF) Phase transfer function Φ (PTF) Frequency convolution theorem: }{}{ 2 1 }{ hFfFhfF ⊗=⋅ π Example: Transform of a Gaussian wave packet. akkxikax ekFee a xE 4/)( 2 00 2 )(,)( −−−− =×= π Please prove it.
    37. 37. 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.
    38. 38. Imaging Task 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. 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
    39. 39. 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) Contrast I I I I = − + max min max min 0 200 400 600 800 1000 0 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
    40. 40. Nyquist Sampling Theory 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!) Sample Intervals in Phase InputWaveformSampledOutput Samples Out of Phase InputWaveformSampledOutput
    41. 41. Optical MTF 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 (λ) 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
    42. 42. System MTF 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. 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
    43. 43. System MTF 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 m cycles mrad km( ) [2. ] [6 ] tan[ / ] ≈ ÷ = 4 1 10 4
    44. 44. Measurement: Knife Edge 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. Edge Response Line Spread Differe -ntiate
    45. 45. Measurements of Image Quality • PSF = Point Spread Function • LSF = Line Spread Function • CTF = Contrast Transfer Function • MTF = Modulation Traffic Function
    46. 46. Point Spread Function PSF • “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
    47. 47. Quantifying Blurring • Object point becomes image circle • Difficult to quantify total image circle size – difficult to identify beginning & end of object Intensity ?
    48. 48. Quantifying Blurring Full 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 Half Maximum
    49. 49. Line Spread Function LSF • Line object image blurred • Image width larger than object width Intensity ?
    50. 50. Contrast Response Function CTF 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.
    51. 51. Contrast Response Function CTF or CRF • Blurring causes loss of contrast – darks get lighter – lights get darker Lower Frequency Higher Frequency Higher Contrast Lower Contrast
    52. 52. Modulation Transfer Function MTF • 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%
    53. 53. 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
    54. 54. MTF • If MTF = 1 – all contrast reproduced at this frequency Recorded Contrast Contrast provided to film
    55. 55. MTF • If MTF = 0.5 – half of contrast reproduced at this frequency Recorded Contrast Contrast provided to film
    56. 56. MTF • If MTF = 0 – no contrast reproduced at this frequency Recorded Contrast Contrast provided to film
    57. 57. 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. Intensity Intensity DisplacementDisplacement
    58. 58. 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
    59. 59. 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 of the Point Spread Function / Line Spread Function. 1.0 Cut-off Spatial frequency
    60. 60. 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
    61. 61. 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.
    62. 62. MTF measurement methods: 1] Point source METHOD Xe lamp: 3kW Xe lamp: 1kW
    63. 63. 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
    64. 64. 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
    65. 65. • 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 6 8 10 12 14 Edge detection Pixels Pixels Curve inflection point Least square fit line
    66. 66. 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
    67. 67. MTF measurement methods: Periodic target Opportunity to acquire Center radial target THRESHOLD (5m) THRESHOLD (2.5m)
    68. 68. APPLICATIONSAPPLICATIONS The MTF curves are used to characterize photographicThe MTF curves are used to characterize photographic objectives and are determined by the comparison of inputobjectives 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 casesWith this study the procedure is also extended to cases where the characterization of the acquisition system is notwhere the characterization of the acquisition system is not possible.possible. ?ACQUISITION SYSTEM OUTPUT IMAGE INPUT IMAGE ? MTF(f) ω, f ACQUISITION SYSTEM OUTPUT IMAGE INPUT IMAGE MTF(f) ω, f
    69. 69. AIM:AIM: extension of the traditional MTF technique to evaluate theextension 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.
    70. 70. "“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
    71. 71. 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 fH fOTFfMTF ==  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.
    72. 72. 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
    73. 73. 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)
    74. 74. Thanks so much. It has been a pleasure. Enjoy the meeting! AJAL.AJ, ME . Assistant Professor METS School of Engineering University of Calicut Mala , Thrissur ( Dt ) Email: 4u.ajal@gmail.com

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