# Lecture 8 - Characterizing an Additive Device

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• Three colour channels
• usually red, green, blue
• 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
1. C(RGB) -> C(RGB) + A
2. C1(RGB) -> C1(RGB) + A
3. C2(RGB) -> C2(RGB) + A
4. 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
1. 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

2. Sometimes dependence is big. Then there are only two recourses
1. Get a new display.
2. 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

1. Chromaticities of the phosphors
1. Maybe you get them from the manufacturer
2. 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
2. The value of gamma
1. 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.
2. Measure Y
3. Plot log(Y) against log(R[GB])
4. It should be a straight line, the slope of which is gamma
3. The normalization constants
1. Turn on the three primaries together to get white
2. Measure the chromaticity of the display, which is its colour temperature
3. Measure the luminance and calculate X, Y, Z
4. Calculate the inverse of the matrix of chromaticies
5. 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.

1. Use the inverse equation above.
A_R           X
A_G = [M^-1]  Y
A_B           Z
2. Divide each element of the resulting vector by the corresponding normalization factor
(R/R0)^g = A_R / e_R

and so on.

3. Take the logarithm
log(R/R0) = (1/g) * log(A_R/e_R)

and so on

4. 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.

## 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

• high efficiency

## Plasma Display Panel (PDP)

### Fuorescent Lights

They consist of

1. A gas tube coated on the inside with a phosphor.
2. It is filled mostly with inert gases, to which a small amount of mercury vapour is added.
3. 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.