cs781 - Colour for Computer Graphics - Winter 2012
Course Notes
Lecture 8 - Characterizing an Additive Device
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A Generic Additive Device
- Three colour channels
- Channels combine by additive mixture
- C(RGB) ~ C1(RGB) + C2(RGB) + C3(RGB)
- The components of the combination are independent of time and
space.
- Channels are independent of one another
- C(RGB) ~ C1(R) + C2(G) + C3(B)
- Each channel provides a constant chromaticity
- C(RGB) ~ ( E1(R) * C_1 ) + ( E2(G) * C_2 ) + ( E3(B) * C_3 )
- Channels track with a common exponent
- C(RGB) ~ ( e1 * (R/R0)^g * C_1 ) + ( e2 * (G/G0)^g * C_2 ) + ( e3 *
(B/B0)^g * C_3 )
These assumptions must be checked and the size of deviation quantified.
We are, of course, going to calibrate using physical measurements., In
terms of typical physical measurements the colour matches might be equivalent
to
- P(RGB) (l) = ( e1 * (R/R0)^g * P_1 (l) ) + ( e2 * (G/G0)^g * P_2 (l) )
+ ( e3 * (B/B0)^g * P_3 (l) )
Possible Defects of Generic Devices
- Channels do not combine by additive mixture. Example, ambient light
- C(RGB) -> C(RGB) + A
- C1(RGB) -> C1(RGB) + A
- C2(RGB) -> C2(RGB) + A
- C3(RGB) -> C3(RGB) + A
Correct equation to
- C(RGB) ~ C1(RGB) + C2(RGB) + C3(RGB) - 2*A
- Spatial and temporal variation
- To increase brightness light is deliberately concentrated in the
direction of the viewer(s).
- As long as there is no variation in chromaticity it's not very
visible.
- Not visible = doesn't matter
- Supply voltage varies
- As long as the variation is slow it's not very noticeable
- Slow means time constants >> 100 milliseconds
- Channels are not independent
- There is almost always a lack of independence caused by
- feeding several channels from a single power supply
- blooming of the electron beam
- interreflections in the face plate
Small dependence can be handled as a correction
- Sometimes dependence is big. Then there are only two recourses
- Get a new display.
- Use subtractive methods, which are discussed later.
- Channels do not have constant chromaticity
- Almost never a problem of physics, chemistry or electrical
engineering.
- Can be caused by blooming
- usually fixed by turning down and brightness and/or
contrast.
- Excitation is not a gamma function
- If exponents are different, which is common, let them be
different.
- If the form is not exponential a table might be better.
Tristimulus Values
- X = \int_l x(l) * P_l dl = \int_l x(l) * \sum_i ( ei * (Ri/Ri0)^g * P_i
(l) ) dl
= \sum_i ( ei * (Ri/Ri0)^g ) * \int x(l) * P_i (l) dl
The integrals, suitably normalized, is just the x chromaticity
coordinate of the phosphor.
- That is, X = \sum_i ( ei * (Ri/Ri0)^g ) * x_i
Note that this is actually a matrix equation
X x_R x_G x_B e_R (R/R0)^g
Y = y_R y_G y_B e_G (G/G0)^g
Z z_R z_G z_B e_B (B/B0)^g
What do We Measure
- Chromaticities of the phosphors
- Maybe you get them from the manufacturer
- More likely, and better, you measure them at several values,
turning on only one primary.
- If they are not constant, you probably have a background to
subtract
- The value of gamma
- Turn on each primary in turn to many levels
- If you notice clipping at high and/or low values, which is
likely,
- censor the data,
- note the true range of useful values of the primary.
- Measure Y
- Plot log(Y) against log(R[GB])
- It should be a straight line, the slope of which is gamma
- The normalization constants
- Turn on the three primaries together to get white
- Measure the chromaticity of the display, which is its colour
temperature
- Measure the luminance and calculate X, Y, Z
- Calculate the inverse of the matrix of chromaticies
- Multiply the measured tristimulus values by the chromaticity matrix
to give
e_R (R/R0)^g X
e_G (G/G0)^g = [M^-1] Y
e_B (B/B0)^g Z
Of course, the multiplicatinve factors, (R/R0)^g
,
(G/G0)^g
, and B/B0)^g
should be equal
The constants required to calculate the tristimulus values without further
measurement are now known.
Getting RGB from the Tristimulus Values
More often we know what tristimulus values should appear on the screen,
and want to know what to write into the frame buffer.
- Use the inverse equation above.
A_R X
A_G = [M^-1] Y
A_B Z
- Divide each element of the resulting vector by the corresponding
normalization factor
(R/R0)^g = A_R / e_R
and so on.
- Take the logarithm
log(R/R0) = (1/g) * log(A_R/e_R)
and so on
- Exponentiate
R = R0 * (A_R/e_R)^(1/g)
It is common to find that R/R0 > 1. Then the desired colour cannot be
produced by the display. What to do in that case is addressed later in the
course.
Other Additive Devices
Colour LCD
These are widely used because they occupy little volume, use little
energy, and weigh little compared to CRTs. Their colour performance is
comparable to CRTs, but the structure of the images they produce can be
intrusive
Technological basis
- backlight
- polarizers
- liquid crystal between the plates of a capacitor
- colour filters
What if we had four filters?
- Why? We are surely overdoing the blue
Colour OLED
Solid state photodetectors and LEDs are very closely related
Plasma Display Panel (PDP)
Fuorescent Lights
They consist of
- A gas tube coated on the inside with a phosphor.
- It is filled mostly with inert gases, to which a small amount of
mercury vapour is added.
- Electrodes at each end of the tube
They make light by
- ionizing the internal gases so that current flows
- This is called electrostatic breakdown.
- as current flows collisions with electrons excite mercury atoms to high
energy states
- decay of these states emits untraviolet light at 180 nm and 240 nm.
- the phosphor absorbs the ultraviolet photons going into high energy
states
- decay of these states emits visible photons.
PDPs
A PDP is an array of electrodes and phosphors which, in the off state
maintain a gas just below it breakdown level.
Fluorescent light is turned off and on by applying varying voltages to the
electrodes.
Thus, a PDP is in effect an array of tiny fluorescent lamps..
Field Effect Display (FED)
Just as the PDP is an array of tiny fluorescent lamps, an FED is an array
of tiny CRTs.
- A vacuum is made in a thin flat volume.
- On one face is phosphor-coated glass and a transparent anode.
- On the other face is an array of tiny cathodes.
- Between the two is an array of gates (like the screens in an ordinary
CRT), one per cathode.
- The screens modulate the current deposited in the phosphor closest to
its cathode.
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