2013 LMIC Imaging Workshop. Sidney L. Shaw Technical Director. - Light and the Image - Detectors - Signal and Noise

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1 2013 LMIC Imaging Workshop Sidney L. Shaw Technical Director - Light and the Image - Detectors - Signal and Noise

2 The Anatomy of a Digital Image Representative Intensities Specimen: (molecular distribution) Optical Image: (collected light that interacts with or eminates from the molecules in the distribution. Digital Image: (a representation of the light energy quantized in space and for relative intensity)

3 Light is a many splendered thing. Light is vectoral and has properties of both a wave and a particle. Some properties of light energy : wavelength frequency polarization collimation coherence interference

4 Light interacts with matter. When light collides with matter, it creates a lot of vocabulary words. The interactions can be characterized as: absorption reflection diffraction refraction dispersion

5 Understanding the spatial scale of the molecular distribution in your specimen.

6 Image Formation: When light originating at a specimen is focussed on to a plane, the distribution of light intensities, together with positive and negative interference, yield an image. Constructive (everything in between) Destructive (

7 Image Formation: All lenses have a finite resolving limit related to the maximum angle of light collection or convergence. All objects smaller than that limit look about the same size. Very small objects form spots of a predictable (diffraction limited) size. Original Object Screen (

8 Image Formation: That minimum spot size for the lens leads to critical limitations for an optical system starting with the resolution limit. Diffraction Limited Spot Intensity Cross Section Converging set of Diffraction Limited Spots Airy Disk and part of a Point Spread Function When is this considered one spot or two spots? Recall the actual molecular size could be much smaller than the size of the Airy disk.

9 Image Formation: The resolution limit of the lens cannot be overcome by simply magnifying the spots.

10 Image Formation: The minimum spot size also plays a significant role in generating image contrast. Let us now replace the set of spots with a set of parallel lines. Black and White High Contrast Gray Low Contrast Rela&ve Spot Size

11 Contrast and Resolution are related in the optical image: The Contrast Transfer Function Distance Contrast = 22% Contrast = 50% Contrast = 100% Ç Contrast = 100% Contrast = 50% Contrast = 22% Modula&on Transfer Func&on Ç Distance (Spacing) 1/Distance (Frequency) Stelzer, 1998

12 The Anatomy of a Digital Image Representative Intensities Specimen: (molecular distribution) Optical Image: (collected light that interacts with or eminates from the molecules in the distribution. Digital Image: (a representation of the light energy quantized in space and for relative intensity)

13 Digital Image: Sampling the optical image into discrete spatial units (pixels). Sampling the light intensity at each position into discrete values (grey levels). General Rule: you need minimally 2-3 pixels per Airy disk to capture the optical resolution to the digital image. Unit

14 Digital Image: Sampling the optical image into discrete spatial units (pixels). Sampling the light intensity at each position into discrete values (grey levels). General Rule: you need minimally 2-3 pixels per Airy disk to capture the optical resolution to the digital image. Unit

15 Detectors come in multiple flavors. The most common ways to capture images are using a digital camera or a PMT. CCD = Charge Coupled device CMOS = Complemenary Metal Oxide Semiconductors PMT = Photo-Multiplier Tube Unit

16 Detector properties that we care about: Quantum Efficiency: % of λ photons converted to electrons Sensitivity Spectrum: Quantum efficiency at a specific wavelength Dark Current Noise: Specified as the rms e - /sec Readout Noise: at a readout speed in rms e - Readout speed: Bits out in hertz (bits per second) khs or mhs Maximum e - or Voltage: in appropriate units CCD and CMOS cameras will also have a pixel size and number. Unit

17 A CCD is a silicon chip partitioned into little electron collecting wells in a grid pattern. Each well captures a limited number of electrons and holds them until readout. At readout, the electrons are forced off the silicon chip where each row of the grid is streamed out as a voltage. e- Voltage e- e- e- Unit

18 In scanning microscopy, the laser light is scanned and the signal is read in a raster pattern. Each scan line yields a PMT voltage proportional to the fluorescence intensity. Voltage

19 The voltage from the PMT or the camera pixels is subsequently sampled both in time and for voltage to create a series of picture elements (pixels). Pixel Posi&on 255 Digital Image Voltage Gray Level Value Pixels 64 0 Pixels Unit

20 The detector converts photons to photo-electrons which appear as a Voltage. A computer converts the (analog) voltage to a (digital) gray level over a discrete area (pixel) using an analog to digital (A/D) converter. 1 The A/D converter is a fancy voltage divider that does a series of binary tests. Voltage Unit

21 The A/D converter uses sequential binary voltage gates. Each gate has only 1 of 2 answers: Yes = 1, No = 0. This example is a 5 bit system yielding 2 5 (0-31) intensity levels. The end result is a binary code (bits) specifying a unique gray level. Gate Voltage Bits The A/D converter is a fancy voltage divider that does a series of binary tests Bits Vals 1 x 16 = 16 0 x 8 = 0 1 x 4 = 4 0 x 2 = 0 0 x 1 = Unit

22 The intensity information is saved to a computer file where 8 bits = 1 byte. An 8 bit image with 512 x 512 pixels will use: 512 x 512 = 262,144 pixels 262,144 x 8 = 2,097,152 bits (or 260 kbytes or ¼ megabyte) A 12 bit image with 512 x 512 pixels will use: 262,144 x 16 = 4,194,304 bits (or 524 kbytes or 1/2 megabyte) because the 12 bit information must be saved in a 16 bit data file. A binary encoded pixel in a 12- bit image = 1,351 1,351 = Byte Byte 16 Bits Unit

23 Why are some images 8 bit and others 12 or 16 bits? How do I know if this value is really different from that value? What factors go into converting the light intensity to a gray level. Unit

24 There are 3 major sources of uncertainty with the pixel intensity value. Thermal Noise: Electrons on the camera/detector that appear randomly due to heat (radiation) in the camera chip/pmt head. Readout Noise: Electrons that are introduced in to the system when electricity is used to push the photoelectrons off the camera chip or drive the voltage of the PMT. Photon Noise: Photon emission is stochastic (exponential) in time resulting in a Poisson distribution of intensities from identical measures. (Also refered to as Shot Noise) Unit

25 There are 3 major sources of uncertainty with the pixel intensity value. If no light is presented to the detector, the electronic noise will appear as random fluctuations for each pixel. The distribution should be Gaussian (Normal). The mean can be considered a background and the standard deviation of the mean value serves as our measurement of the noise. Histogram of Pixel Values Mean = 45 StD = 10 Unit

26 There are 3 major sources of uncertainty with the pixel intensity value. Readout noise depends upon how fast the image is read out and is independent of exposure time. Thermal noise increases with exposure time. N e = N e + N r The noise adds in quadrature to yield an average measure of uncertainty. Histogram of Pixel Values Mean = 45 StD = 10 Unit

27 There are 3 major sources of uncertainty with the pixel intensity value. Photon (shot) noise increases with the square root of the signal. As the total signal increases, the shot noise becomes a smaller percentage of the overall intensity. Low signal means high uncertainty. Histogram of Pixel Values Unit

28 So here is the important slide about understanding gray level (intensity) values. Maximum electrons per pixel well = 120,000e Total (avg) electronic noise = +/- 25e 120,000e/25e = 4,800 If each pixel intensity (gray) level equaled 25 photoelectrons, we could discriminate about 4,500 gray levels Could be a 12- bit (4,096) system But a 16- bit (65,536) system is overkill This A/D converter might be set to have 12 gates with the smallest being set to 25 electrons. Bits Gray Levels 16 = 2 16 = 65, = 2 14 = 16, = 2 12 = 4, = 2 10 = 1,024 8 = 2 8 = = 2 6 = 64 4 = 2 4 = 16 2 = 2 2 = 4 Unit

29 So here is the important slide about understanding gray level (intensity) values. Maximum electrons per pixel well = 120,000e Total (avg) electronic noise = +/- 7e 120,000e/7e = 17,143 If each pixel intensity (gray) level equaled 7 photoelectrons, we could discriminate about 17,000 gray levels Could be a 14- bit (16,384) system Bits Gray Levels 16 = 2 16 = 65, = 2 14 = 16, = 2 12 = 4, = 2 10 = 1,024 8 = 2 8 = = 2 6 = 64 4 = 2 4 = 16 2 = 2 2 = 4 This A/D converter might be set to have 14 gates with the last gate set to ~7 electrons. Unit

30 In summary Each pixel spacially samples a part of the optical image. The pixel contains both photo-electrons and accumulated noise electrons. A conversion factor is used to divide the total electron count into a representative (gray level) value. The conversion factor should take the detector noise properties into account so that there is some confidence the detected values are different. That leaves the photon noise. Signal = avg(want to see) Background = avg(don t want to see) Noise = st. dev.(don t want to see) SNR = Signal - Background Noise Signal to Noise Ratio (SNR) is the critical value for determining the quality of the digital image. e- e- e- e- Unit

31 Estimating Signal and Noise from your image data. Shaw 2006

32 Look Up Tables (LUT) and Image Display (34,34) (34,129) (34,102) (153,153) (153,255) (153,255) Output to Screen 0 Output to Screen Output to Screen 0 0 Input Value from Image Input Value from Image Input Value from Image

33 Look Up Tables (LUT) and Image Display (34,34) (34,129) (34,102) (153,153) (153,255) (153,255) 16.4 / / / / / / Output to Screen 0 Output to Screen Output to Screen 0 0 Input Value from Image Input Value from Image Input Value from Image

34 File pixel values (i) Display Image Values Look Up Tables (LUT) and Image Display Changing the apparent contrast of an image is often done by modifying the look-up table. You do it in Photoshop all the time. So what is legal and what isn t? It depends upon the point you are trying to make from the image. Explain everything you did to make the image presented for review.

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