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Topics: Statistics The Human Visual System Color Science Radiometry/Photometry Geometric Optics Tone-transfer Function Image Sensors Image Processing Displays & Output Colorimetry & Color Measurement Image Evaluation Psychophysics Outline Definition of Terms and Units Radiometry Solid Angle, Point Sources, Projected Area Sources of Radiation Gas Discharge Fluorescent Blackbody Radiation Incandescent The Sun and daylight SOURCES LABORATORY Outline Radiance Radiance invariance Lamberts Cosine Law and Lambertian Surfaces Relationship between radiance and exitance Relationship between flux and intensity Photometry and Color Temperature HVS short overview Photometric terminology Planckian locus Color temperature Distribution temperature Outline Spectral radiometry Diffraction gratings Spectrometers Wavelength selectors Absorption and interference filters IR rejection ND filters Monochromators CALIBRATION LABORATORY Irradiance Variation with Distance and Angle Point source (inverse square law) Line source Plane source Outline Irradiance Variation with Distance and Angle Point source (inverse square law) Line source Plane source INV SQ LAW LABORATORY Outline Radiometry and Imaging Systems Non-Point Sources Lens falloff and exposure Irradiance onto the focal plane How to handle non-point source calculations Some governing formula’s Integrating Spheres (if time permits) Governing sphere equation Applications of integrating spheres Spectroradiometry Emmett Ientilucci, Ph.D. Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science Spectroradiometry- Overview Diffraction Gratings Line spacing, lpm Grating types Order convention Spectrometers Monochromators Spectral Considerations n(l) = speed in vacuum c speed in medium v(l) -n, will always be greater than one -So, the index is a function of wavelength -Therefore, the amount of refraction is different -This effect is called chromatic dispersion n(l) d Normal Dispersion Region 1.5 1.0 0.4 0.7 1.0 l Dispersing Prism d is the deviation angle What is a Diffraction Grating? Simply another device to disperse polychromatic light Extension of Young’s double slit experiment Is based on both diffraction and interference 2nd-order maximum 1st-order maximum 0th-order maximum D Relative Brightness Slits widths are not much greater in width than the wavelength of light So, what is a Diffraction Grating? Extension of Young’s double slit Instead of two slits, we not have N small transmitting slits that are comparable to the wavelength of light. Move from 2-slit to N-slit interference problem Reflection Grating + 1 - + 2 2 Monochromatic Beam 1 -qr qi d - It is clear that ray 2 travels a greater distance than ray 1 which is the general grating equation using the pos/neg angle conventions above. Properties Location of the m = 0 order: When the incident angle, qi = 0: Lines per Millimeter The distance, d between grooves would be Distance can also be expressed as L - is the total length of the grating N - is the total number of grooves How lpm does a DVD have? Grating Equation Observations As the number of slits increases the PM narrows and gets sharper. The principal maxima (PM) are called spectrum lines 2 Slits 4 Slits See grating applets: http://library.thinkquest.org/26938/diff.html http://www.physics.uq.edu.au/people/mcintyre/applets/grating/grating.html 20 Slits What is the Geometry of This Pattern? Spectrum Red Using a two wavelength source l1 = 400 nm Blue l2 = 600 nm Red Blue Order Convention Pos Orders + - Neg Orders m=0 qi + - a+1 qi a+1 -qr a-1 a-1 -qr m=0 + - Spectrometer A spectroscopic instrument that may scan wavelengths individually or the entire spectra simultaneously. It may employ a prism or grating for means of dispersing incident light. Grating Spectrometer Comes in many configurations Grating Spectrometer Ocean Optics USB 650 25 um Slit 200-1100 nm range Spectral Calculation Spectral Calculation Neutral Density Filters - Absorbs light uniformly in VIS - Can vary exposure while maintaining a particular focus Transmission = 10-ND ND = -log(transmission) http://dvdreamtime.com.au/images/tiffen/ndcompare580433.jpg IR Cut Filters Simply blocks NIR radiation and passes VIS radiation Why you would want to do this? Can be done via absorption filters Optical glass that is absorptive in the NIR Can be done via reflection filters Short-pass interference filters that reflect NIR Typically block 640 – 1100 nm (i.e., NIR) IR Cut Filters Reflective Filters Absorptive Filters http://www.optics-online.com/OOL/pics/IRCcurve40.gif Reflective Filters (For Security Cameras) CALIBRATION LABORATORY Irradiance Variation with Distance and Angle Emmett Ientilucci, Ph.D. Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science Irradiance Falloff From a Point Source Lets use some radiometric terms to defines useful expressions How does the irradiance vary with distance from a point source? E2 = (E1 r12) / r22 [W / m2] This formula only works with the following assumptions You have a point source Non intervening medium (transmission = 1) Photons travel in straight lines The flux from the first distance is the same flux at the second distance. Irradiance Falloff From a Point Source What if I knew the flux per solid angle? How is irradiance related to this? Intensity, I [W /sr] Irradiance, E [W / m2] Solid Angle, [sr] Distance, r ? ? ? E = I / r2 [W / m2] Example Using Sun And Earth Irradiance Falloff from a Line Source How does irradiance vary from a line source? What is a line source? Infinite number of point sources next to each other So, we just need to be far enough away to consider it a line (use our factor of ten rule) E2 = (E1 r1) / r2 i.e., 1 inch tube, place yourself 10 inches away (don’t want to see extents of the tube) [W / m2] Irradiance varies inversely with distance Assumptions It is infinite in length Transmission is one Plot of 1/xn Irradiance Falloff From a Plane Source What is a flat, plane, broad source? Infinite number of point sources on (x,y) plane E2 = E1 Irradiance does not vary from an infinite plane source INV SQ LAW LABORATORY Radiometry and Imaging Systems Emmett Ientilucci, Ph.D. Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science Lens Falloff To this point We have done radiometry in the absence of imaging Lets incorporate what we know about radiometry with the simplest of imaging systems Pinhole camera http://www.dkimages.com/discover/previews/756/196161.JPG Spam Pinhole Camera Pinhole http://zedomax.com/blog/tag/pinhole_camera/ Lens Falloff – Ideal Camera For a simple system like this, what is the “uniformity” like on the image plane? Uniform Radiance (e.g., 18% Gray Card) Lens Falloff This is for a lens-less pinhole system The lens helps to reduce optical vignetting The cos q due to the effective smaller aperture Therefore, a lens system typically has n < 4. Lens Falloff http://en.wikipedia.org/wiki/Image:RioparaguayJune2005.jpg To Compensate, use Anti-vignetting filter Exposure would be too long, if one used a “perfect” Anti-vignetting filter Trade off between level of “uniformity” and exposure Vignetting A derived term from vignette From the same root as vine (French) Originally referred to a decorative border in a book Later, used to describe a photographic portrait which is clear in the center, and fades off at the edges. Vignetting A decrease in geometrical transmission A reduction in the illumination at some image point (usually off-axis) Vignetting 3 types of vignetting Optical Natural Both of these are inherent to each lens design Collectively, these are referred to as “lens falloff” Mechanical Due to the use of improper attachments to the lens Does not produce “gradual” falloff Abrupt transition with entirely black image corners http://www.vanwalree.com/optics/vignetting.html Vignetting Optical Vignetting Strongest when the lens is used wide open Stopping down can reduce optical vignetting But You collect less light for off-axis points hence image corners will be darker. http://www.vanwalree.com/optics/vignetting.html f/1.4 f/5.6 Vignetting Natural Vignetting Natural light falloff, cos4 q Our “Lens falloff” derivation Remember, not all four cosines may be present Inherent to each lens design and becomes more troublesome for wide angle lenses (i.e., short f) Is not cured by stopping down Stopping down helps “optical vignetting” Can help fix “natural vignetting” with anti-vignetting filter http://www.vanwalree.com/optics/vignetting.html Vignetting Mechanical Vignetting Mechanical extensions (e.g., lens hood) to a lens protrude into its FOV Lens hood prevents flare http://www.vanwalree.com/optics/vignetting.html Camera Equation We Camera Equation A way to relate the radiance at the front of a camera system to the irradiance at the focal plane Metric of optical throughput G# = L/E [sr-1] Lens System Aperture Camera System Focal Plane Camera Equation Factoring in system element variables we have: Valid for: On optical axis For small apertures (i.e., large f/#) Focused at infinity Transmission is uniform Camera Equation Camera equation of ANY f-number: Valid for: On optical axis Focused at infinity Transmission is uniform For off-axis conditions, Reduce irradiance by cos3q Area / Non-Point Sources Emmett Ientilucci, Ph.D. Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science Area Sources What is an area source? How do we perform radiometry when point source approximations produce large errors? source-radius to source-distance is small? Overview Energy Exchange Between Parallel Disc’s Small disc source and small receiver (pt source solution) Large disc source and small receiver (non-pt source solution) Comparison of point source and non-point source solutions Examples Energy Exchange Between Paralled Plates Large plane source and small receiver Large plane source and large receiver Energy Exchange Between Arbitrary Surfaces Derivation of G# for Small f-number’s Energy Exchange Between Parallel Disc’s What is the flux from a Lambertain source of radiance L, onto a receive at distance r? We will first use point source approximations…..that is, we are at least 10 x the radius of the source (i.e., 1% error). Energy Exchange Between Parallel Disc’s From the viewpoint of the “source” L F0 Energy Exchange Between Parallel Disc’s Now calculate when the distance is small compared to the source radius Now, what is the flux from a small segment annulus? Assume “it” is a point source. Then integrate over all small segments Energy Exchange Between Parallel Disc’s If source is Lambertian, (i.e., no L(x,y)), the Non-Point Source case yields: Where q1/2 will be the “half-angle” or ½ the FOV (same as q in all our figures) Non-Point Source Case (rectilinear coordinates) Point Source Case: q Recall, from point source solution, Ratio the fluxes….. If distance “r” is big, they are the same Using our point source rule, r = 10R We get a 1% error. Example 1 What is flux on receiver ? Example, with a Lambertian blackbody, (D) diameter = 1.2m, T=320 K. Receiver is a 0.05 m diameter at a distance, r = 3m. Assume t=1 R r L Note: 0.6m x 10 = 6m We are at 3m. -Can’t use pt source approx. Integrating Spheres Emmett Ientilucci, Ph.D. Digital Imaging and Remote Sensing Laboratory Chester F. Carlson Center for Imaging Science Integrating Spheres Integrating Sphere Used to spatially integrate radiant flux Internal or external source or radiation Integrating Sphere Applications Include: Light collection from internal or external source (called lamp measurement photometry) Uniform light sources Laser power measurement LED spectral and flux measurement Reflectance of either specular or scattering samples Total or diffuse-only transmittance measurement Cosine receptor Irradiance From an Ideal Integrating Sphere Want to relate flux from source to total irradiance exiting sphere Assume: - Entrance/exit port are small - Baffles/wires, etc are also small - Inside surface is Lambertian and uniform r F Irradiance From an Ideal Integrating Sphere 5 5 4 3 1- 2 1 1 0 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 Reflectance 0.7 0.8 0.9 1 1 Ideal Integrating Sphere, Example Find efficiency of a source -Measure irradiance -Measure electrical power (16) Real Integrating Spheres Baffle Baffle Baffle Detector Not perfectly Lambertian Specular Reflection Baffles Integrating Sphere Coating Coating types offered by Labsphere Total Flux from a Source Can be configured for Photo- or Radiometric measurements (integrated or spectral) Diffuser - Originated at turn of 20th century - Fast, simple, method for comparing output of different lamps. Calibrated Photopic Detector 2/3 r Sphere Photometer - What is flux from source? LASER and LED Power Measurements - Detectors can’t handle laser power density - Integrating sphere prevents damage - LED (divergent or non-symmetric beam) - Overfill active detector area - Integrating sphere spatially integrates Laser Or LED Detector - What is the LASER power? Cosine Receptor - Ideal Diffuser - Due to its insensitivity to angular alignment, integrating spheres make excellent ‘collectors’ Protective Weather Dome Monochromator Detector Global Irradiance Monitor -What is the irradiance / illuminance of a horizontal surface? Total Transmittance of Sample Optional Monochromator Irradiation Beam Sample Detector Baffle t= SignalSAMPLE SignalOPEN PORT (No sample) Diffuse Transmittance of Sample Optional Monochromator Irradiation Beam Sample Detector t= SignalSAMPLE SignalOPEN PORT (No sample) Baffle Specular Trap Same as before, with added specular trap Total Reflectance or Sample Optional Monochromator q = Up to 10o Irradiation Beam = q SSAMPLE Baffle SREF (Halon) Detector Sample Collects specular and diffuse component Diffuse Reflectance of Sample q = Up to 10o Optional Monochromator Optional Monochromator q = 0o Irradiation Beam Specular Trap Irradiation Beam q Baffle Detector Sample Collects diffuse component Detector Sample Collects diffuse component Uniform Source Radiance Standard - Many tungsten halogen lamps placed near port - Must have a regulated current supply