Characterisation of a desktop LCD projector

Characterisation of a desktop LCD projector

Y. Kwak, L. MacDonald*

Colour and Imaging Institute, Kingsway House East, University of Derby, Derby DE22 3HL, UK

Received 24 July 2000; revised 24 July 2000; accepted 7 September 2000

Abstract

A typical desktop LCD projector was characterised. Having determined the optimum settings of the brightness and contrast

controls, measurements were made with a spectroradiometer to establish the additivity of the primaries, inter-channel dependence,

colour gamut, tone scale, contrast, spatial non-uniformity, temporal stability and viewing angle variation. Four mathematical models

were compared for their accuracy in predicting the colours generated by the display for arbitrary signal inputs. A new model was

developed for the S-shaped electro-optical transfer function of the LCD device, and was extended to predict the anomalous colour

tracking of the primaries. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: LCD display; Projection display; Characterisation; Electro-optic transfer function; Mathematical modelling

1. Introduction

The characterisation of colour-imaging devices is an

essential procedure in the design of colour reproduction

systems [1]. Characterisation of an output device de®nes

the relationship between the device signal space and the

colours generated, speci®ed in terms of the CIE system

[2]. Thus for an LCD projector, it de®nes the relationship

between the voltages quantised as data input to the

projector and the colours displayed on the screen. The

characterisation may be de®ned as a mathematical

model based on a set of equations or a de®nition of discrete

points that constitute a look-up table. The characterisation

result depends on the calibrated state, which means the

setting up of a device or process so that it gives repeatable

data [2,3].

In the case of conventional CRT displays, theoretical

characterisation models are well established. However, it

has been proven that the GOG model, which is widely

used for CRT monitor characterisation, is not suitable for

¯at panel LCD-based monitors [4]. Therefore it is likely that

an LCD projector, which also uses liquid crystal light valves

to produce colours, would have different characteristics

from a CRT monitor.

There is as yet no standard characterisation method

for projection media, although a proposal has been

made by the International Electrotechnical Commission

(IEC) Project Team 61966. The ®rst working draft [5]

was published in 1998, but little progress has been

made. Some of the assessment methods proposed in

this study were based on the IEC draft, although various

details were changed.

In this study both calibration and characterisation for an

LCD projector were performed. The effect of the brightness

and contrast controls of a typical desktop LCD projector,

Sanyo PLC-5605B, were examined to ®nd the optimum

setting for the large dynamic range and tone reproduction.

Then, with this optimum setting, the characterisation for the

LCD projector was performed using the traditional CRT

characterisation techniques Ð GOG model and LUT

model. Also new empirically derived mathematical

characterisation methods were tried. The characterisation

results of these models were compared using a set of test

colours.

2. Conditions

2.1. Environmental conditions

Every measurement was carried out in a dark room.

One hour warm up time was allowed preceding any

measurement.

Displays 21 (2000) 179±194

0141-9382/00/$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.

PII: S0141-9382(00)00049-4

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* Corresponding author. Tel.: 144-1332-622217.

E-mail address: [email protected] (L. MacDonald).

2.2. Conditions of measurements

2.2.1. Equipment

(1) LCD projector Ð Sanyo PLC-5605B

Dimensions

(W £ H £ D)

260 mm £ 159 mm

£ 391 mm

Net weight 5.9 kg

LCD panel system 1.3 00 TFT active matrix type

(thin ®lm transistor) £ 3

Number of pixels 1,557,504 {519,168 (832 £ 624) £ 3}

Scanning frequency H-sync. 15 , 80 kHz, V-sync.

50 , 100 Hz

Projection image size

(diagonal)

Adjustable from 20 00 to 400 00

Contrast ratio 100:1 (ANSI)

Horizontal resolution 750 TV lines

Projection lens F2.5 , 3.2 lens with

f47 mm , 75 mm

motor zoom and focus

Throw distance 1.1 m , 14.3 m

Projection lamp Metal halide, 120 watt type

Projection mirror Dichroic mirror and X-prism system

Image elevation

adjustment

Up to 68

(2) Screen

Hardboard painted with Dulux vinyl matt white emulsion

paint

Size: 120 cm £ 120 cm

Colour: ®ve points were measured using re¯ectance

spectrophotometer X-Rite 938

Y x y Lp ap bp

Average 90.49 0.3176 0.3354 96.20 20.61 8.19

Stdev 0.07 0.0001 0.0001 0.03 0.04 0.13

(3) Spectroradiometer Ð Photo Research PR-650

Type Multi-channel

spectroradiometer

Spectral range 380±780 nm

Angle of view 18

Wavelength resolution , 3.5 nm/pixel

Spectral bandwidth 8 nm

Photodetector element 128 elements

Luminance range (cd/m2) 3.4±17,000

Spectral accuracy ^ 2 nm

Luminance accuracy (A) ^ 4% ^1

Chromaticity accuracy ^ 0.0015x, ^0.001y

(4) Laptop computer Ð Samsung Sense 820 (PC

compatible)

Display Card: Mach64LT

Display Driver: RAGE LT PRO AGP 2x

Resolution: 1024 £ 768

Colour: High Colour (16-bit)

2.2.2. Image geometry

Side view

Top view

Test images. Except for the screen uniformity test, all

measurements were performed on a central uniform square

patch �h=5 £ h=5 , 17:6 £ 17:6 cm; h: the effective screen

height) with the remainder of the display ®lled with a

black background represented by RGB digital counts of

(0,0,0). All displayed images on the screen were made

using Microsoft PowerPoint software.

2.2.3. Measured data

The absolute tristimulus values for 28 observers were

measured for all displayed colours. The data from PR-650

are accurate to four signi®cant digits.

2.2.4. Zoom control

To minimise the optical effect of the lens, the zoom

control was set to the middle position.

Y. Kwak, L. MacDonald / Displays 21 (2000) 179±194180

2.2.5. Effects of the `contrast' and `brightness' controls

2.2.5.1. Luminance changes.1 By adjusting the `contrast'

and `brightness' controls on the LCD projector, dynamic

range and tone reproduction characteristics may be changed.

The relationship between the `contrast' and `brightness'

settings and the performance of the LCD projector was eval-

uated to ®nd out the optimum setting condition. In the Sanyo

PLC-5605B, the values for the `contrast' and `brightness'

controls can be changed from 0 to 63. At ®rst, the luminance

changes for black and white colour were examined for the nine

combinations of minimum (0), middle (32), maximum (63)

values of `Contrast' and `Brightness' (Table 1).

As `Brightness' was increased without changing `Contrast',

the luminance values for both black and white colours also

increased. When `Contrast' was increased without changing

`Brightness', luminance was increased for white but for

decreased black. This showed that the function of the `Bright-

ness' control was to raise the overall luminance for every

digital count and of `Contrast' was to increase the slope

between the brightest and darkest colour as shown in Fig. 1.

When `Brightness' was low, the luminance of white was

also lowered, therefore the dynamic range was reduced. When

`Brightness' was too high, the darkest point was also increased

so dynamic range was reduced again. In the case where

`Contrast' was too low, dynamic range was reduced and

where too high, clipping occurred for dark and bright colours.

Fig. 1 shows this effect where there are no luminance changes

for digital count changes at each extremity. (The graphs of Fig.

1 are just to aid understanding of the functions of `Contrast'

and `Brightness' and do not show the exact relationship

between digital count and luminance.)

When `Brightness' was changed from 32 to 63, the black

point increment was much higher than for the change from 0

to 32. Also in the case of `Contrast' 63, there were no

changes in white point between `Brightness' 32 and 63.

So the optimum setting of `Brightness' has to be near to

or lower than 32. When `Contrast' was changed from 32

to 63, black point decreased and white point increased.

However, it had to be checked whether clipping occurred

between `Contrast' 32 and 63. Therefore there must be an

optimum point for dynamic range and tone reproduction

between `Brightness' 0±32 and `Contrast' 32±63. Supple-

mentary measurements were made to ®nd the optimum

Y. Kwak, L. MacDonald / Displays 21 (2000) 179±194 181

Table 1

Luminance changes by contrast and brightness setting I

Setting Luminance (cd/m2) Dynamic range� �W 2 B�=B

Contrast Brightness Black White

0 0 0.5624 54.90 96.62

0 32 0.8404 93.16 109.85

0 63 3.2770 118.70 35.22

32 0 0.4101 103.00 250.16

32 32 0.5419 152.00 279.49

32 63 1.5090 159.80 104.90

63 0 0.4065 139.60 342.42

63 32 0.4501 157.00 347.81

63 63 0.9283 156.60 167.70

Fig. 1. Effects of `Brightness' and `Contrast' changes and clipping effect.

Table 2

Luminance changes by contrast and brightness setting II

Setting Luminance (cd/m2) Dynamic range� �W 2 B�=B

Contrast Brightness Black White

40 32 0.4633 153.8 330.97

45 32 0.4615 154.8 334.43

50 32 0.4277 154.3 359.77

55 32 0.4781 156.8 326.96

60 32 0.4497 157.4 349.01

63 32 0.4501 157.0 347.81

1 The measurement data used in Sections 2.2.5 and 4.4 were obtained

from different measurement conditions. Therefore the data is not identical

with that of other experiments.

point. After `Contrast' 55, there were no luminance changes

for white, so `Contrast' has to be lower than 55 (Table 2).

Tone reproduction curves were than measured for the

combinations 55±32, 0±63 and 32±32 (`Contrast'±

`Brightness' settings). Fig. 2 shows that although 55±32

had the largest dynamic range, 32±32 had a more linear

relationship between digital count and luminance, and

therefore better tone reproduction. Consequently 32±32

was chosen to the `standard' setting.

Except in the Warm-up experiment, for the characterisa-

tion of this LCD projector, both the `Contrast' and `Bright-

ness' controls were always set to 32.

2.2.5.2. Chromaticity and correlated colour temperature

change.1 When `Brightness' and `Contrast' settings were

changed, not only luminance but also the chromaticity and

correlated colour temperature (CCT) of white changed in

response. When luminance was increased, CCT was

lowered. This relationship is more clear when the spectral

data is analysed (Fig. 3). As luminance is increased,

increments of green wavelengths are larger than blue or

red wavelengths. This may be due to the characteristics of

the ®lters used to make primary colours in the projector, or

to the liquid crystal material itself (Table 3).


Fig. 2. Luminance (left) and CIELAB: Lp (right) value changes for grey colours under different `Contrast' and `Brightness' settings.

Table 3

Relation between contrast and brightness setting and chromaticity of white

Setting Chromaticity

Contrast Brightness Y (cd/m2) u 0 v 0 CCT (K)

0 0 54.90 0.1722 0.4446 11362

0 32 93.16 0.1733 0.4557 9509

0 63 118.70 0.1740 0.4632 8612

32 0 103.00 0.1733 0.4620 8783

63 0 139.60 0.1757 0.4721 7718

32 32 152.00 0.1775 0.4755 7292

63 63 157.00 0.1777 0.4811 6986

Fig. 3. Spectral radiance for white under different `Contrast' and `Bright-

ness' settings.Fig. 4. The spectral radiance distributions for peak colours red, green and

blue.

Table 4

Chromaticities of the primary and white colours

R G B X Y (cd/m2) Z x y u 0 v 0

Black 0 0 0 0.38 0.47 0.55 0.2706 0.3372 0.1777 0.4798

White 255 255 255 114.60 137.50 134.10 0.2967 0.3560 0.4359 0.5307

Red 255 0 0 33.45 18.10 0.66 0.6407 0.3467 0.1311 0.5747

Green 0 255 0 57.47 112.00 5.47 0.3285 0.6402 0.1789 0.1366

Blue 0 0 255 23.99 8.15 130.10 0.1479 0.0502 0.1664 0.4665

Correlated colour temperature for white: 7073 K

3. General characterisation measurements

3.1. Spectral characteristics

The spectral radiance of white was measured for three

different settings of contrast and brightness controls, as

plotted in Fig. 4. The chromaticities of black, white and

the three primary channels are given in Table 4.

3.2. Additivity

The additivity of the display for all three tristimulus

values (Y� luminance) was examined by comparing the

tristimulus values for white screen with the sum of the

tristimulus values of the individual red, green and blue

primaries (Table 5).

Even for a black colour, the LCD projector emits some

light. This must be due to a small amount of energy that

`leaks' through the LCD cells, as explained by Fairchild [4].

This leaked light is always added to a displayed colour.

However, the amount is small enough to ignore for white

so this effect is not considered for the additivity test. The

results indicate that additivity is well preserved, although

the reason for the slight lack of additivity for the Z value is

not known.

3.3. Inter-channel dependence

The inter-channel dependence between the input data

and the tristimulus values of displayed colours was evaluated

according to the method recommended by the IEC [5].

3.3.1. De®nition

X 0

Y 0

Z 0

0BB@1CCA � S´

R

G

B

0BB@1CCA � S´T

1

R

G

B

RG

GB

BR

RGB

0BBBBBBBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCCCCCCA

;


Table 5

Additivity test result

X Y (cd/m2) Z

White 114.60 137.50 134.10

R 1 G 1 B 114.91 138.25 136.23

Difference (%) 0.27 0.54 1.59

Fig. 5. Colour gamut boundary in xy and u 0v 0 plane.

Fig. 6. Colour gamut boundary in CIELAB space.

where

S �0:241 0:417 0:172

0:129 0:814 0:056

0:001 0:036 0:945

0BB@1CCA

² X 0, Y 0, Z 0: measured CIE tristimulus values of light

output, normalised to the measured luminance value for

peak white.

² R, G, B: normalised monitor luminance levels computed

using the spectral radiance of the red, green, and blue

channels at maximum excitation as primaries.

² S: 3 £ 3 matrix which de®nes the dominant linear rela-

tionship between monitor luminance levels and output

CIE tristimulus values.

² T: 3 £ 8 matrix which de®nes cross-channel relations

among red, green and blue channels.

3.3.2. Method of measurement

The 32 centred colour patches were displayed and

measured. These consisted of eight steps of grey and four

steps each of red, green, blue, yellow, magenta and cyan.

At � S´T´Dt

where

3.4. Colour gamut

Colour gamuts of the LCD projector, based on the

measured primary and secondary colours, are shown in

the xy and u 0v 0 plane and in the CIELAB colour space

(Figs. 5 and 6).

The boundaries for primary colours in Chroma-Lightness

co-ordinates were determined from the measurement of red,

green and blue channel. The average hue angles were

33:5 ^ 9:78 for red, 129:1 ^ 16:98 for green and 308:0 ^

7:58 for blue. The large hue angle variation arises from the

signi®cant changes of chromaticities of each channel with

input level (Section 3.6).

3.5. Tone characterisation

Tone characterisation means establishing the electro-

optical transfer function, which describes the relationship

between the signal used to drive a display channel and the

luminance produced by that channel. Electro-optical trans-

fer functions were evaluated for red, green, blue and grey

channels. For each channel, output luminances of 32 steps

were measured from digital counts 8±255 with increment 8

(Fig. 7).


D �

1 Dr1 Dg1 Db1 Dr1Dg1 Dg1Db1 Db1Dr1 Dr1Dg1Db1


..

. ... ..

. ... ..

. ... ..

. ...


0BBBBBBB@

1CCCCCCCA

A �

X 01 Y 01 Z 01

X 02 Y 02 Z 02

..

. ... ..

.

X 032 Y 032 Z 032

0BBBBBBB@

1CCCCCCCATherefore

T � S21Át´�Dt�21 � S21´��Dt´D�21´DtÁ�t

�20:0023 1:0033 20:0011 0:0032 0:0004 20:0019 20:0043 0:0030

20:0008 0:0008 1:0011 0:0005 20:0012 20:0007 20:0006 0:0009

0:0000 0:0002 0:0002 1:0000 20:0021 20:0002 20:0002 0:0023

0BB@1CCA

Fig. 7. Electro-optical transfer functions of three channels.

3.6. Colour tracking characteristics

Chromaticity changes of primary colours and achromatic

colours depending on the drive signal level of each channel

were evaluated. For each channel eight steps were measured

and the resulting data were reported on the CIE 1976 UCS

diagram (u 0,v 0).Fig. 8 shows that the chromaticities of each channel

varied with input level and approached that of black as

the input level approached zero because the chromaticity

of black arises from the leaked light through LC cells and

this leaked light is always added to any colour. Therefore

the chromaticities could be corrected by subtracting the

black values (Fig. 9).

If the chromaticities of the primaries were constant, the

chromaticities should vary along a straight line from maxi-

mum point to black point and after black correction the

chromaticities from each channel should fall on the same

points. However, Figs. 8 and 9 show that chromaticities

varied as functions of the luminance levels of primary

lights. Blue exhibited the largest variation, followed by

green. Red showed the most stable chromaticity.

The changes of the spectral radiance distributions

with luminance levels seem to explain this phenomenon.

For blue and green primaries, humps can be observed in

their spectral radiance distribution graphs (see Fig. 4).

These regions did not change linearly with other parts

of the graphs according to the change of input digital

values, hence the change of chromaticity. The loci for

chromaticity changes of primaries are accurately

predicted using the S-curve model II (Section 5.4).

4. Assessment measurements

4.1. Contrast

The display contrast was measured using the `checker-

board' method recommended by ANSI [6]. With this

method, a 4 £ 4 checkerboard pattern was generated consist-

ing of black and white rectangles that cover the entire image

area, as illustrated in Fig. 10. The luminance at the centre of

each rectangle was measured. The eight white values were

averaged together, as were the eight black values. The

contrast ratio Cwas then calculated by using the average

white value L0 and the average black value Lb in terms of

the Weber±Fechner fraction

C � L0 2 Lb

Lb

The table below shows the measured luminance corre-

sponding to each position of the ANSI checkerboard (unit:

cd/m2)

Average (cd/m2) Black:White W±F fraction

Black 1:415 ^ 0:162 1:91.61 90.61

White 129:6 ^ 7:8

The black to white ratio 1:91.61 was smaller than the ratio

1:100 given in the manufacturer's speci®cation of the LCD


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5u’

Grey

Red

Green

Blue

Fig. 8. Changes of chromaticities of the primaries.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0 0.1 0.2 0.3 0.4 0.5’

RedGreen

Blue

Grey

Fig. 9. Chromaticities of the primaries after black correction.

Fig. 10. ANSI checkboard pattern for contrast measurement.

projector because the settings of `Contrast' and `Brightness'

were not optimum for maximum dynamic range and the

speci®cation of the LCD projector does not de®ne the screen

condition for the contrast measurement. Note that the black

to white ratio under these conditions is much lower than if

calculated from measurements of full white and full black

screens (1:291.0, data from Table 8), because of ¯are from

the white areas.

4.2. Spatial non-uniformity

The LCD projector uses an optical integrator to produce

uniform illumination of the light valve and therefore, in

principle, nearly uniform illumination of the projection

screen [7]. In reality, however, the integrator makes the

illumination leaving the projection lens nearly uniform,

but not necessarily the luminance distribution on the screen.

The projector is evidently designed for use on a table top,

with a wall-mounted screen whose mid-point is signi®cantly

higher than the height of the projector (Section 2.2.2). The

image ®eld is projected upwards, with asymmetrical angles

of 16.48 above and 2.58 below the horizontal axis. The light

from the projector therefore reaches different locations on

the screen at different distances from the lens, reducing the

luminance proportional to the reciprocal of square of the

distance. Because of this intrinsic character of the projector,

the luminance of a projected image cannot be spatially

uniform. The spatial non-uniformity of an image produced

by the LCD projector was evaluated by measuring tri-

stimulus values of 25 points of image white and calculating

the colour differences (see Fig. 11).

Measurement data is shown in Table 6. CIELAB colour

differences were calculated using the values of point 13 as a

reference white.

Tables 6 and 7 indicate that the image colour (or purity of

white) varied according to the position. The image ®eld on

the screen could thus be divided into three regions with

distinctive colour distributions in xy and CIELAB space

were examined, as shown clearly in Fig. 12.

If spatial non-uniformity were caused only by the differ-

ences of optical paths, colorimetric distribution would be

symmetric in the horizontal direction. However, the colour

cast between the right and left sides of the image suggests

some defect in the illumination system or in the optical

alignment of this particular LCD projector.

4.3. Spatial independence

Spatial independence refers to the impact that a colour

displayed in one area of the screen has on another colour. To

evaluate the spatial independence of the LCD projector, a

method proposed by Fairchild was employed [4]. A set of

colour stimuli was de®ned, including black (0,0,0), grey

(128,128,128), white (255,255,255), red1 (128,0,0), red2

(255,0,0), green1 (0,128,0), green2 (0,255,0) and blue1

(0,0,128), blue2 (0,0,255). Each of the nine colour stimuli

was measured on nine different backgrounds made up of the

same set of colours.


Fig. 11. Measurement points for spatial non-uniformity.

Table 6

Measurement data (Yxy) for spatial non-uniformity test

1 2 3 4 5

1 Y 112.3 119.1 117.8 120.3 114.2

x 0.3003 0.3036 0.3056 0.3073 0.3043

y 0.3614 0.3649 0.3680 0.3779 0.3730

2 Y 126.1 128.6 128.8 130.9 125.3

x 0.2997 0.3005 0.3014 0.3035 0.3054

y 0.3616 0.3608 0.3628 0.3747 0.3785

3 Y 134.4 134.5 138.8 138.0 133.9

x 0.2988 0.2967 0.2981 0.2997 0.3042

y 0.3608 0.3538 0.3579 0.3680 0.3769

4 Y 135.1 139.8 141.9 141.1 136.1

x 0.2954 0.2951 0.2946 0.2974 0.3017

y 0.3548 0.3523 0.3533 0.3626 0.3702

5 Y 134.5 141.3 143.8 143.1 137.0

x 0.2922 0.2937 0.2936 0.2965 0.2980

y 0.3490 0.3502 0.3512 0.3620 0.3616

Table 7

CIELAB colour difference distribution in the display

1 2 3 4 5

1 DLp 27.91 25.77 26.17 25.40 27.30

Dap 20.36 20.15 20.45 23.79 23.18

Dbp 1.64 3.53 4.99 8.88 6.45

2 DLp 23.65 22.91 22.86 22.24 23.89

Dap 20.80 20.01 20.41 24.57 25.08

Dbp 1.66 1.54 2.44 7.23 8.87

3 DLp 21.24 21.21 0.00 20.22 21.38

Dap 20.94 1.15 0.00 23.69 25.10

Dbp 1.22 21.84 0.00 4.11 8.21

4 DLp 21.04 0.28 0.86 0.64 20.76

Dap 20.03 0.96 0.17 22.60 23.61

Dbp 21.69 22.72 22.44 1.65 5.31

5 DLp 21.21 0.69 1.38 1.19 20.50

Dap 0.85 1.16 0.61 22.81 21.75

Dbp 24.51 23.83 23.45 1.25 1.36


Fig. 12. Variation in image chromaticity.

Table 8

Measurement data of standard colours for spatial independence test

Colour R G B X Y Z Lp ap bp Cp

Black 0 0 0 0.40 0.48 0.59 1.53 0.10 22.59 2.59

Blue1 0 0 128 6.29 2.07 32.58 12.49 66.31 275.61 100.57

Red1 128 0 0 5.32 3.12 0.61 16.68 37.97 23.14 44.47

Blue2 0 0 255 23.81 8.16 129.40 29.00 100.73 2119.95 156.64

Red2 255 0 0 35.29 19.15 0.63 43.81 78.18 69.61 104.68

Green1 0 128 0 10.66 21.23 1.62 45.90 241.38 60.86 73.60

Grey 128 128 218 21.62 25.44 34.43 49.75 1.95 213.69 13.83

Green2 0 255 0 57.62 112.90 5.27 92.05 270.09 118.34 137.54

White 255 255 255 116.30 139.70 134.30 100.00 0.00 0.00 0.00

Table 9

Lightness differences DLp by different background colours

DLp Stimulus Avg

Black Blue1 Red1 Blue2 Red2 Green1 Grey Green2 White

Background Black 0.00 21.13 20.06 20.07 20.42 20.56 20.59 20.67 20.84 20.48

Blue1 20.06 0.00 20.03 20.31 20.54 20.62 20.43 21.19 21.03 20.47

Red1 0.16 21.00 0.00 20.22 20.56 20.69 20.65 21.03 21.06 20.56

Blue2 0.88 1.54 0.15 0.00 20.81 20.84 20.54 20.93 21.34 20.21

Red2 3.30 0.49 1.33 0.37 0.00 20.30 20.64 20.87 20.86 0.31

Green1 2.81 0.27 0.89 0.40 20.20 0.00 20.52 20.71 21.43 0.17

Grey 3.54 1.62 1.05 0.69 20.51 20.08 0.00 20.90 20.84 0.51

Green2 11.69 5.77 5.34 2.95 1.33 2.36 1.87 0.00 20.08 3.47

White 13.78 8.74 6.64 3.47 1.92 2.82 3.04 0.10 0.00 4.50

Average 4.01 1.81 1.70 0.81 0.02 0.23 0.17 20.69 20.83 0.80

The measured tristimulus values were converted to

CIELAB values using the white colour as a reference

white. Then colour differences were calculated for each

colour stimulus. For the calculation of colour difference,

the colour patch with the same coloured background was

used as a standard. The measurement data are tabulated in

Table 8, sorted by the magnitude of luminance.

Table 9 shows the lightness differences DLp, demonstrat-

ing that lightness of the stimulus was directly affected by the

lightness of the background colour. The largest differences

are for dark stimuli with light backgrounds, maximum being

black stimulus with white background.

Table 10 shows the CIELAB colour differences DEpab:

Overall the average CIELAB colour difference was 6.10

indicating that there is a large spatial dependence for the

LCD projector. Colour differences were largest when the

background colour had high chroma (Green2, Blue2) and

high lightness. This spatial dependence probably arose

from the illumination system of the LCD projector, ¯are

from the screen and re¯ections from the walls or other


Table 10

CIELAB colour difference DEpab by different background colours

DEpab Stimulus Avg

Black Blue1 Red1 Blue2 Red2 Green1 Grey Green2 White

Background Black 0.00 6.56 0.40 0.88 0.78 0.97 6.40 2.11 1.82 2.21

Blue1 6.76 0.00 6.18 0.41 7.57 4.83 0.51 4.12 1.97 3.59

Red1 2.74 6.86 0.00 0.62 1.05 1.50 5.50 1.73 1.93 2.44

Blue2 21.53 6.59 19.19 0.00 20.49 14.58 7.16 8.15 2.45 11.13

Red2 15.74 8.24 3.84 1.51 0.00 3.97 6.04 2.88 1.99 4.91

Green1 7.81 11.87 4.00 1.68 1.79 0.00 7.79 1.42 1.83 4.24

Grey 3.57 4.50 5.40 2.01 7.46 4.13 0.00 3.37 1.41 3.54

Green2 27.16 30.79 16.93 11.40 6.12 4.31 12.98 0.00 0.80 12.28

White 14.19 15.04 13.63 12.24 17.20 9.75 5.88 6.73 0.00 10.52

Average 11.06 10.05 7.73 3.42 6.94 4.89 5.81 3.39 1.58 6.10

Fig. 13. Tristimulus values and CIELAB Colour Differences for a full white and a medium grey colour. `Contrast' 0, `Brightness' 63 was used for this

experiment.

objects in the room. To ®nd out which factor is the

most signi®cant, more research is needed. But for quan-

titative applications, especially for using projected

images in a psychophysical experiment, this effect

should be well understood.

4.4. Temporal stability1

The warm-up characteristics of ¯at panel LCDs were

evaluated by Fairchild and Wyble. The results showed

that the output tristimulus values for the white colour

increased quickly initially and then reached a very stable

level after about 45 min. However, the output levels for the

grey patch increased signi®cantly at the beginning and then

started to decrease and never reached a completely stable

level during the full 4-h evaluation [4].

The LCD projector was checked using the same measure-

ment method as for the ¯at panel LCD. A full white

(255,255,255) and a medium grey (128,128,128) were alter-

nately displayed and measured every 2 min. These measure-

ments began from a cold start (initial power-up of the LCD

projector) and continued for about 40 min.

It is clear from Fig. 13 that the characteristics of the

LCD projector were not similar to the ¯at panel LCD.

Tristimulus values for white and grey showed good stability

from the beginning, with steady state reached after about

10 min.

4.5. Viewing angle characteristics

The dependence of luminance on horizontal viewing

angle was evaluated for 11 test colour patches Ð 7 grey

levels, peak white, peak red, peak green and peak blue

(Fig. 14). The luminance of each colour was measured

successively over a speci®ed range of horizontal viewing

angles (in 108 increments) from the normal viewing direc-

tion to ^408.

Test colour R G B

Grey1 32 32 32

Grey2 64 64 64

Grey3 96 96 96

Grey4 128 128 128

Grey5 160 160 160

Grey6 192 192 192

Grey7 224 224 224

Peak white 255 255 255

Peak red 255 0 0

Peak green 0 255 0

Peak blue 0 0 255

The result showed that, unlike normal projection screens,

this painted white matt screen has minimal angular depen-

dence except for a slightly higher re¯ectance at the normal

direction and no colour dependent angular characteristics.


Fig. 14. Lumiance changes by horizontal viewing angle.

The luminance of white at 408 from normal was reduced by

about 8% relative to the normal direction.

5. Characterisation

To characterise the LCD projector, Sanyo PLC-5605B for

`Contrast' 32, `Brightness' 32 settings, three methods were

used Ð PLCC model, GOG model and a new S-curve

model. The performances of these three methods were

evaluated using 94 test colours by comparing the measured

data with the values predicted by each model.

5.1. PLCC model

The PLCC model is based on work of Post and Calhoun,

which was later evaluated by Johnson et al. [2]. This model

uses piecewise linear interpolation assuming constant chro-

maticity co-ordinates. This is implemented by separate

LUTs for each channel and assumes that the relationship

between the DAC (digital-to-analogue converter) value

and the output luminance is linear between the points in

the LUT.

The electro-optical transfer function data (Section 3.5)

was used to construct three one-dimensional look-up tables.

Altogether 33 data points (31 steps, zero and maximum 255)

were used for each channel. For each combination of input

red, green, blue (R,G,B) digital values, the corresponding

tristimulus values (X,Y,Z) for each channel were calculated

using linear interpolation and then summed.

5.2. GOG model

The GOG model, devised by Berns [8,9] for CRT

displays, shows the relationship between digital input values

and the CIE tristimulus values of light emitted by phos-

phors. The GOG model consists of two stages non-linear

relationship between DAC signal values and monitor R,G,B

luminance levels, followed by a linear transformation

matrix where the R,G,B channel luminances are transformed

to CIE tristimulus values X,Y,Z.

Non-linear relationship between DAC values and monitor

luminance values is de®ned as:

R �kg;r´dr 1 ko;r

h igr

; kg;r´dr 1 ko;r

h i$ 0

0; kg;r´dr 1 ko;r

h i, 0

8><>:9>=>;

± dr; dg; dh: normalised input digital values for red, green

and blue channels

Analogous equations can be set up for the Green and Blue

channels

± kg,r, kg,g, kg,b: Model gain. Overall system gain terms

relating DAC values dr, dg, db to CRT monitor lumi-

nance level R, G, B, respectively

± ko,r, ko,g, ko,b: Model offset. Overall system gain terms

relating DAC values dr, dg, db to CRT display lumi-

nance level R, G, B, respectively

± g r, g g, g b: Gamma. The exponents in the non-linear

relationship between CRT grid voltages and beam

currents.

± R, G, B: Normalised monitor luminance levels

computed using the spectral radiance of the red,

green, and blue channels at maximum excitation as

primaries

Linear transformation matrix is then de®ned

Xpixel

Ypixel

Zpixel

26643775 �

X

Y

Z

26643775

ambient flare

1

X

Y

Z

26643775

inter-reflection flare

1

Xr;max Xg;max Xb;max

Yr;max Yg;max Yb;max

Zr;max Zg;max Zb;max

26643775

R

G

B

26643775

Using this model, after ®nding the model gain, offset

and gamma of each red, green, blue channel, the output

colour generated by any input digital value can be

predicted. To estimate the necessary model parameters,

two data sets were used: (1) data for 32 colours from

red, green and blue channels; (2) data for only 8 colours

from each channel. Even at zero input signals Ð black

colour Ð there is some leakage of light from the LCD

projector. So to calculate the parameters, the tristimulus

values of black were subtracted from all measurement

data and then added back again to calculate the ®nal

output values. (This black correction was also done for

the PLCC model.) The linear transformation matrix

used in the calculation was:

Xpixel

Ypixel

Zpixel

26643775 �

0:3776

0:4705

0:5471

26643775 1

33:07 57:09 23:61

17:63 111:5 7:675

0:1113 4:925 129:6

26643775

R

G

B

26643775

At ®rst using the linear transformation matrix,

measured X,Y,Z tristimulus values were converted to

monitor luminance levels R,G,B. Then the measurement

data for the red channel was used to calculated R

values, and similarly for G and B. Finally the model


Table 11

Coef®cients for GOG model

Using 32 colours Using 8 colours

Red Green Blue Red Green Blue

Gain kg 1.43 1.49 1.49 1.48 1.51 1.51

Offset ko 20.38 20.44 20.44 20.46 20.48 20.48

Gamma g 1.70 1.33 1.33 1.46 1.22 1.22

parameters were calculated using the `Solver' function

in Microsoft Excel (Table 11).

The measured and predicted values for 32 colours used as

training data were compared in terms of their CIELAB

colour differences. Generally each channel gave poor

performances. Especially for the green and blue channels,

the colour differences were more than double those of the

red channel. There was little performance difference

between the two data sets (i.e. using 32 colours vs. using

8 colours) (Table 12).

5.3. S-curve model I

The shapes of the electro-optical transfer function of

conventional CRT monitor and LCD-based display or

projector are quite different [10]. The CRT follows a

power function but the LCD typically has an S-shaped

curve (Section 3.5), as depicted in Fig. 15.

The GOG model is based on the intrinsic behaviour

(gamma function) of the CRT. But the LCD light valve is

controlled electrically in a very different way from the CRT,

so it is not surprising that the performance of the GOG

model for LCD projector is so poor. To characterise the

LCD projector more effectively, a new mathematical

model is now proposed, which will be called S-curve

model I.

The S-curve model has the same two-stage structure as

the GOG model but uses a different function for the non-

linear relationship between DAC signal values and display

RGB luminance levels, i.e. the electro-optic transfer func-

tion. The proposed hyperbolic function is a mathematical

construction, suggested by analogy with Hunt's use of a

similar function for retinal cone responses [11], except

that a second exponent has been included to allow for differ-

ent curvature at the black and white ends.


luminance values

R � Ar

darr

dbrr 1 Cr

; G � Ag

dagg

dbgg 1 Cg

; B � Ab

dab

b

dbb

b 1 Cb

± dr, dg, db: normalised input digital values for red, green

and blue channels

± R, G, B: normalised display luminance levels

computed using the spectral radiance of the red,

green, and blue channels at maximum excitation of

the primaries.

The model parameters were calculated using same proce-

dure as for GOG model (Table 13).

The measured values and the predicted values for 32

colours used as training data were compared in terms of

CIELAB colour differences. Note that very good results

were obtained with only 8 grey colours used to calculate

the model parameters (Table 14).


Table 12

GOG model testing result using training colours

Using 32 colours DEpab Using 8 colours DEp

ab

Red Green Blue Average Red Green Blue Average

Avg 3.91 7.57 12.51 8.00 4.82 8.55 13.36 8.91

STDEV 4.04 9.11 9.87 5.31 11.00 11.71

Max 16.35 37.63 42.67 22.12 46.70 52.30

Fig. 15. Electro-optical transfer functions of CRT and LCD based monitors.

Table 13

Coef®cients for S-curve model I

Using 32 £ 3 colours Using 8 £ 3 colours Using 8 grey colours

Red Green Blue Red Green Blue Red Green Blue

A 3.54 2.37 2.09 3.39 2.55 2.20 3.85 2.62 2.15

a 3.29 3.20 3.15 3.31 3.16 3.12 3.30 3.16 3.09

b 11.77 6.94 7.85 10.78 7.17 7.96 10.37 7.49 7.87

C 2.55 1.39 1.12 2.39 1.55 1.20 2.77 1.63 1.17

The S-curve model showed dramatically improved

performance compared to the GOG model, in terms of the

greatly reduced DEpab values. The relatively poor perfor-

mance of the blue channel can be explained from colour

tracking characteristic of the LCD projector used in this

study. The linear transformation used in the GOG and

S-curve I models assumes constancy of the channel

chromaticity for any input level. However, the chroma-

ticities of blue and green channels did change for different

input levels (Section 3.6). Therefore the S-curve I and GOG

models must always have some residual errors caused by

chromaticity changes.

5.4. S-curve model II

In the S-curve model I, it was assumed that the normal-

ised monitor luminance levels are independent each other.

Therefore R, G and B were functions only of dr, dg and db,

respectively. However, the measurement data showed that

the R, G and B are not perfectly independent. This means,

for example, that the input signal to the blue channel

affects not only B but also R and G luminance values.

This effect is represented in Fig. 16, which shows negli-

gible change for the red channel but large changes for the

green and blue channels, and therefore the relatively poor

performance of S-curve Model I for blue and green

channels.

The normalised monitor luminance level driven by

another channel is small when it is considered that the

vertical axis of Fig. 16 has a scale from 0 to 1. However,

to predict the colour tracking characteristics accurately and

to improve the tone characterisation performances for green

and blue channels, this component must be included in the

characterisation model. It is observed from Fig. 16 that all

curves have a similar form, which appears to follow the

gradient of the S-curve function. The function for the non-

linear relationship between DAC values and monitor

luminance levels was therefore extended by adding to

each term a component based on the ®rst derivative of the

other two channels.


luminance values

R � Arr´fR�dr�1 Arg´fG0�dg�1 Arb´fB

0�db�

G � Agr´fR0�dr�1 Agg´fG�dg�1 Agb´fB

0�db�

B � Abr´fR0�dr�1 Abg´fG

0�dg�1 Abb´fB�db�

f �x� � xa

xb 1 C; f 0�x� � �a 2 b�xa1b21 1 aĆ´xa21

�xb 1 C�2f 0(x) is the ®rst-order derivative of f(x)

² dr, dg, db: normalised input digital values for red, green

and blue channels.


Table 14

S-curve model I testing result using training colours

Using 32 £ 3 colours DEpab Using 8 £ 3 colours DEp

ab Using 8 grey colours DEpab

Red Green Blue Avg Red Green Blue Avg Red Green Blue Avg

Avg 1.06 2.30 4.78 2.71 1.05 2.31 4.79 2.72 1.12 2.32 4.48 2.64

STDEV 0.58 0.89 2.82 0.55 0.93 2.87 0.59 0.92 2.54

Max 2.52 4.01 8.00 2.52 4.47 8.24 2.58 4.24 7.72

Fig. 16. Normalised monitor luminance level generated by input signal from the other two channels. R by Dg means R value generated by green channel input

signal.

² R, G, B: normalised monitor luminance levels computed

using the spectral radiance of the red, green, and blue

channels at maximum excitation of the primaries.

Using this new function, the CIELAB colour differences

between measured and predicted values for the training

colours were calculated.

The results in Tables 15 and 16 show a further improve-

ment for both green and blue channels. Note that each

channel now has similar size of CIELAB colour differences.

Using this S-curve model II, the colour tracking chromati-

cities were predicted (Section 3.6). The result in Fig. 17

shows a good match between predicted and measured

values, compared to Fig. 8. Note that Agr and Abr were set

to 0 because of their negligible contribution.

5.5. Comparison of the model performances

The accuracy of these four methods Ð PLCC, GOG

models and S-curve model I, II Ð was compared using

94 test colours. The measured data were compared with

the values predicted by each model in terms of CIELAB

colour differences. Table 17 summarises the results.

Simple one-dimensional look-up-table showed the best

result followed by S-curve model II and S-curve model I

using eight grey colours and GOG model showed worst

result. By using the S-curve model I, a reasonably good

characterisation result was achieved by measuring the CIE

tristimulus values of only eight grey levels.

6. Conclusions

As described in the introduction, device characterisation

is very important in cross-media reproduction. Many math-

ematical models and techniques for characterisation of

colour-imaging devices have been under development.

However, characterisation of LCD projectors is not well


Table 15

Coef®cients for S-curve model II

Using 32 £ 3 colours Using 8 £ 3 colours

Red (n� R) Green (n� G) Blue (n� B) Red (n� R) Green (n�G) Blue (n� B)

Anr 3.539 20.033 0.016 3.394 20.030 0.016

Ang 0 2.365 20.007 0 2.550 20.007

Anb 0 0.002 2.092 0 0.002 2.203

a n 3.292 3.201 3.147 3.308 3.157 3.118

b n 11.770 6.939 7.851 10.783 7.166 7.956

Cn 2.552 1.389 1.119 2.394 1.551 1.204

Table 16

S-curve model II testing result using training colours

Using 32 £ 3 colours DEpab Using 8 £ 3 colours DEp

ab

Red Green Blue Avg Red Green Blue Avg

Avg 1.06 1.18 1.35 1.18 1.05 1.22 1.29 1.19

STDEV 0.58 1.04 0.98 0.55 1.07 1.02

Max 2.52 4.32 4.37 2.52 4.61 4.63

Fig. 17. Comparison of the colour tracking characteristics between measured and predicted by S-curve model II.

understood. One of the dif®culties is the problem of the

screen, which is not a part of the LCD projector but is an

essential part of the whole projection system. Therefore, the

colour appearing on the screen is determined not only by the

projector but also by the screen. However, separating the

effects of LCD projector and screen is not an easy task. In

this report, the characterisation included both the LCD

projector and the screen. To characterise the LCD projector

itself, excluding the effect of the screen, a different techni-

que would be needed.

The calibration and characterisation for an LCD projec-

tor, Sanyo PLC-5605B, were performed. To maximise the

dynamic range and achieve a linear tone reproduction, the

`Contrast' and `Brightness' controls of the projector were

set to 32 and 32 each. The LCD projector showed imperfect

constancy of channel chromaticity, causing slight chroma-

ticity changes in the blue and green channels by input signal

levels. The ANSI contrast ratio was 1:91. The spatial unifor-

mity test showed that not only luminance but also hue and

chroma changed according to the position in the image. The

darkest part of a white screen had only 78.1% luminance of

the brightest point. Also in the case of projected image, the

colour in the centre was seriously affected by the back-

ground colour. Although, this spatial dependence could be

minimised when achromatic and low luminance colours

were used as background. The warm-up characteristic of

the projector was stable without abrupt changes over time.

The traditional tone characterisation methods for a

CRT monitor Ð PLCC and GOG models Ð were

applied to characterise the LCD projector. Also two

variants of a new method, S-curve model I and II,

were tried. The results showed that the PLCC and S-

curve model II performed better and the GOG model

performed worst.

S-curve model I and II were empirically derived from the

measurement data. However, the function used in the S-

curve model (below) has a very generalised form. When

b is equal to 0, f(x) becomes a power function, which

could be used to characterise a CRT based monitor.

f �x� � Axa

xb 1 C

Even though the performance of the two S-curve models

was slightly worse than PLCC, S-curve model I needed the

data of only eight grey colours instead of the 32 £ 3 colours

that have to be measured for the PLCC model.

Further investigation will be necessary to establish the

theoretical basis of the S-curve function and also the ®rst

derivative terms in S-curve model II. Our belief is that it is

related to the switching behaviour of the liquid crystal light

valves and the birefringence of the liquid crystal material

itself [12]. The derivative terms in S-curve model II mean

that it could be controversial to recommend this as a

standard method for characterising a conventional LCD

projector, even though the model performed very well in

this study. Further studies with other LCD projectors are in

progress to reveal how effective the model is in general.

References

[1] L.W. MacDonald, Developments in colour management systems,

Displays 16 (1995) 203±211.

[2] A. Johnson, Methods for characterising colour scanners and digital

scanners, Displays 16 (1995) 183±191.

[3] J. Morovic, To Develop a Universal Gamut Mapping Algorithm, PhD

thesis, University of Derby, 1998.

[4] M.D. Fairchild, D.R. Wyble, Colorimetric characterization of the

Apple Studio Display (Flat Panel LCD), Munsell Color Science

Laboratory Technical Report, July, 1998.

[5] IEC 61966-6, Colour measurement and management in multimedia

systems and equipment Ð Part 6: equipment used for digital image

projection, Committee Draft, August 1998.

[6] ANSI IT7.215-1992, Data Projection Equipment and Large Screen

Displays Ð Test Methods and Performance Characteristics.

[7] E.H. Stupp, M.S. Vrennesholtz, Projection Displays, Wiley, New

York, 2000, 308±309.

[8] R.S. Berns, R.J. Motta, M.E. Gorzynski, CRT colorimetry, part I:

theory and practice, Col. Res. Appl. 18 (1993) 299±314.

[9] R.S. Berns, Methods for characterizing CRT displays, Displays 16

(1995) 173±182.

[10] L.D. Silverstein, T.G. Fiske, Colorimetric and Photometric Modelling

of Liquid Crystal Displays, IS & T and SID's Color Imaging

Conference: Transforms and Transportability of Color (1993)

149±156.

[11] R.W.G. Hunt, Measuring Colour, 3rd ed., Fountain Press, Kingston-

upon-Thames, 1998, 212.

[12] V.G. Chigrinov, Liquid Crystal Devices: Physics and Applications,

Artech House, Boston, MA, 1999, 104±108.


Table 17

Model performance comparison using 94 test colours

DEpab

PLCC

(32 £ 3)

GOG

(32 £ 3)

GOG

(8 £ 3)

S-curve I

(32 £ 3)

S-curve I

(8 £ 3)

S-curve I

(Grey 8)

S-curve II

(32 £ 3)

S-curve

II (8 £ 3)

AVG 1.29 9.11 10.84 2.18 2.21 1.90 1.55 1.41

STDEV 1.01 6.99 9.80 1.64 1.60 1.49 0.95 0.89

Max 5.70 23.78 33.92 7.32 7.53 7.02 4.39 4.65

Documents

Characterisation of a desktop LCD projector