# Resolution test with line patterns

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1 Resolution test with line patterns OBJECT IMAGE 1 line pair Resolution limit is usually given in line pairs per mm in sensor plane. Visual evaluation usually.

2 Test of optics alone Magnifying glass Test pattern Lens Optical image Eye This gives the resolution of the optics, R optics

3 Test of film alone Test pattern on glass plate Film Exposure Emulsion Development Film Magnifier Eye This gives R film Rule of thumb: 1 R total R 1 optik 1 R film

4 It s difficult to measure resolution of electronic sensors Use back-calculation 1 R total 1 R optik R 1 sensor From experiment Calculated

5 Sensor size matters! Final image Small sensor Final image Large sensor Higher resolution needed for small sensor!

6 Solution Give resolution in line pairs per picture height. Numbers directly comparable regardsless of sensor size, megapixels etc.

7 Resolution tests Advantages: Cheap, simple, easy to understand Disadvantages: Subjective, limited information

8 Resolution numbers don t tell you everything! a) b) Which image would you prefer, a or b?

9 Actually, the resolution is 60 % higher in a than in b!! a) b) You don t believe that? Let s look at a test pattern imaged with cameras a and b a) b)

10 MTF (Modulation Transfer Function) Advantages: Objective Gives a lot of information Disadvantages: Complicated Expensive Idea: Image line patterns of different densities. How much lower is the contrast in the image compared with the object?

11 MTF (Modulation Transfer Function) Line pattern in object Gray level profile Line pattern in image MTF curve Gray level profile

12 We need to quantify pattern density Test patterns with gray level that varies sinusoidally s 0 Spatial frequency (sv. Ortsfrekvens) = (= pattern density) Unit m -1 (or mm -1 )

13 On the website of the course

14 Analogy: Frequency response of an audio amplifier or loudspeaker Amplification frequency (Hertz) Bass (100 Hz) Soprano (10 khz)

15 Object luminance Max Min Object coordinate Degree of modulation, M Max Max Min Min (= Contrast ) Sensor signal Max Min Coordinate in sensor plane M image < M object (loss of contrast) MTF-value = M image /M object

16 An MTF curve shows contrast loss as a function of pattern density 1 MTF value Frequency limit MTF( ) (spatial freq. in sensor plane) Object Image Freq. 1 : M = M 1 M image = M 1 x MTF( 1 ) Freq. 2 : M = M 2 M image = M 2 x MTF( 2 ) = 0

17 Multiplication rule for MTF Lens Spatial frequency mm -1 )

18 MTF depends on F-number MTF F-number (bländartal) Lens: Leica 50 mm/2.0

19 Resolution numbers don t tell you everything! a) b) The resolution is 60 % higher in a than in b!! Let s look at MTF

20 a) b) MTF b) a) Normalized spatial freq.

21 Tangential orientation Image center Radial orientation MTF Center Corner, radial Corner, tangential Normalized spatial freq.

22 MTF at freq. 20 mm -1 MTF at freq. 40 mm F 8 Image corner 1.0 Image corner F 2 F F 2 rad. tang. 0 Distance from image center 0 Distance from image center

23 MTF for photographic film Figure credit: Kodak

24 MTF for electronic sensors 1 MTF 0.8 Ideal sensor Typical real sensor Nyquist frequency Spatial freq. (cycles/pixel)!!! Detector element (pixel). Typically 2-8 m wide 1 cycle/pixel 0.5 cycles/pixel Nyquist freq. = Highest freq. that can be recorded without aliasing (moiré)

25 Anti-aliasing filter MTF Typical sensor Sensor + Anti-aliasing filter OK Moiré Anti-aliasing filter Spatial freq. (cycles/pixel) Result: Much less moiré effects (but they don t disappear completely) AND the filter blurs the image considerably!!

26 Measuring MTF for digital cameras. Photograph edge (avoid sharpening, use RAW format) + computer processing.

27 Object Luminance Pixel value Image MTF Computer processing

28 Real measurements MTF Sensor with med anti-aliasing filter filter Sensor med anti-aliasing filter Sensor + with optik. Bl. anti-aliasing 8 filter + optics at F 8 F 16 OK Moiré Spatial freq. (cycles/pixel)

29 Influence of F-number MTF F-number = 8 F = 4 F = 16 Spatial freq. (cycles/pixel)

30 Center and edge performance MTF Image center Edge Spatial freq. (cycles/pixel)

31 It can be a bit tricky to compare MTF curves for sensors with different sizes and/or Mpixel numbers. If spatial frequency is given in mm -1, sensor size must be taken into account If spatial frequency is given in cycles/pixel, Mpixel number must be taken into account Solution: Use same technique as for resolution Resolution given in line pairs per picture height. Numbers directly comparable regardsless of sensor size, megapixels etc.

32 Give spatial frequency in units of line pairs per picture height MTF Line widths/picture height (= 2 x line pairs/picture height) Curves directly comparable regardsless of sensor size, megapixels etc.

33 Photometric image quality Noise Dynamic range

34 Noise Signal-to-noise ratio, SNR. Uniform grey level (Lab session 5) Photo credit: Kodak

35 Images with different SNR

36 Ultimate limit set by photon quantum noise to where N = number of detected photons per pixel. Typically High ISO setting = Small N max = Noisy image

37 Dynamic range The total span of light levels that can be rendered From white sand on a beach To a black cat in the shadow = max. luminance ratio that can be rendered Typically Compare human eye: (for a good camera) (HDR photography requires several exposures)

38 High dynamic range photography (from Wikipedia, photo credit: Dean S. Pemberton) 6 exposures Combined in one image

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