Simple 3d crosstalk measurement charts

I recently bought a new television capable of passive 3d. When I was trying to select the "best" television I found out there wasn't a proper easy way to measure 3d crosstalk that is the most important feature of 3d technology. It's equally important as stereo crosstalk in audio signals but nowadays most audio signals are so high fidelity that audio crosstalk is basically non-existent.

But 3d technology still has to evolve, still too much crosstalk and to push the technology forward the consumers have to know which technology to buy and which not. One way of doing that is figuring how to measure 3d crosstalk preferable without any meters but visually and doing it so that results are interchangeable between different televisions settings and 3d technologies.

One of important settings will be gamma curve. Some televisions have gamma curve 2.2, some 2.4, others something else. The gamma curve defines how the television shows signals color levels as luminance levels in screen. If gamma curve is 1.0, zero signal shows zero light, 1 signal shows full light and 1/2 signal shows half light. But normal gamma curves used (2.2, 2.3, 2.4 ) means that 1/2 signal is not shown as half light but less than that.

If you don't know what gamma curve your television is set to, it probably is 2.2.

With 3d glasses, left eye sees only picture intended for left eye and vice versa. But technology is not perfect and left eye sees also a little bit of picture intended for the right eye. That is 3d crosstalk and in movies it shows as ghost images.

Static contrast ratio is the ratio between the whitest white and blackest black in static picture. If you have OLED television, then it's contrast ratio is virtually infinite. Others have to live with little imperfection and for instance my televisions static contrast ratio should be about 1:3000. The 3d crosstalk can also be presented as a ratio between the "right" picture and the "wrong" picture.

How test patterns work

In my test patterns I have divided three main colors to separate test charts and both eyes have their own test charts so there are six different test charts. There is also test charts for white color but problem with white test chart is that your television might have for instance more crosstalk for instance blue color so you would have to try to match blue color with white color and it's difficult to do without a meter. It it easier to measure each color separately.

The test charts have the "right" picture that is different patches starting from black patch and moving to patches with more luminance. The "wrong" picture is full white stripes. When you are testing with left-eye-pictures, you put a piece of paper or your hand in front of your right eye to block it and and only your left eye sees the picture through the 3d glasses. Then you see the "right" picture as you should and the "wrong" picture as faint but you can still see the with stripes.

Selecting the right patch

Now you have to select which of the "right" pictures patches equals the "wrong" pictures faint white stripe in luminosity. The faint white stripe is the crosstalk and you are trying to measure it. If it is too difficult to find the correct patch, you can also try to find the first and last patch that look similar as the white patch. Then take the luminosity values from the table below and the right patch is the one that has luminosity (first patch luminosity + last patch luminosity )/2 eg. the average of the two.

Luminosity for patches:

Patch	2,2	2,3	2,4
0	0	0	0
1	5,07705190066176E-006	2,91714209990719E-006	1,67611405153091E-006
2	0,000023328	1,4365692796936E-005	8,84658300141058E-006
3	5,69217657121931E-005	3,65036650558521E-005	2,34096315502103E-005
4	0,0001071874	0,000070745	4,66925450146811E-005
5	0,000175124	0,0001181921	7,97685278983462E-005
6	0,0002615438	0,0001797651	0,0001235568
7	0,0003671363	0,0002562613	0,0001788706
8	0,0004925038	0,0003483891	0,0002464447
9	0,0006381828	0,0004567887	0,0003269532
10	0,0008046585	0,0005820464	0,0004210208
11	0,0009923743	0,0007247042	0,0005292319
12	0,0012017395	0,0008852674	0,0006521366
13	0,0014331346	0,0010642099	0,0007902557
14	0,0016869153	0,0012619788	0,0009440845
15	0,0019634162	0,0014789976	0,0011140959
16	0,0022629532	0,0017156692	0,0013007431
17	0,0025858256	0,0019723778	0,0015044612
18	0,0029323183	0,0022494914	0,0017256693
19	0,003302703	0,0025473632	0,0019647722
20	0,0036972396	0,0028663325	0,0022221612
21	0,0041161771	0,0032067268	0,0024982154
22	0,0045597549	0,003568862	0,0027933027
23	0,0050282035	0,0039530436	0,0031077808
24	0,0055217449	0,0043595678	0,0034419975
25	0,0060405937	0,0047887218	0,0037962918
26	0,0065849574	0,0052407843	0,0041709944
27	0,007155037	0,0057160266	0,0045664279
28	0,0077510274	0,0062147127	0,0049829077
29	0,0083731177	0,0067370998	0,0054207423
30	0,0090214919	0,0072834387	0,0058802336
31	0,0096963287	0,0078539744	0,0063616773
32	0,0103978023	0,008448946	0,0068653632
33	0,0111260824	0,0090685875	0,0073915756
34	0,0118813344	0,0097131276	0,0079405936
35	0,01266372	0,0103827904	0,0085126911
36	0,0134733969	0,0110777953	0,0091081373
37	0,0143105194	0,0117983575	0,0097271968
38	0,0151752382	0,0125446878	0,01037013
39	0,0160677009	0,0133169933	0,0110371927
40	0,0169880521	0,0141154772	0,011728637
41	0,0179364333	0,0149403391	0,0124447112
42	0,0189129834	0,0157917752	0,0131856597
43	0,0199178384	0,0166699782	0,0139517235
44	0,0209511319	0,0175751379	0,01474314
45	0,0220129949	0,0185074407	0,0155601436
46	0,0231035562	0,0194670703	0,0164029652
47	0,0242229421	0,0204542075	0,0172718328
48	0,0253712769	0,0214690304	0,0181669716
49	0,0265486828	0,0225117143	0,0190886036
50	0,02775528	0,0235824322	0,0200369483
51	0,0289911865	0,0246813545	0,0210122224
52	0,0302565189	0,0258086492	0,0220146402
53	0,0315513914	0,0269644822	0,0230444132
54	0,0328759169	0,028149017	0,0241017507
55	0,0342302066	0,0293624149	0,0251868596
56	0,0356143697	0,0306048353	0,0262999445
57	0,0370285142	0,0318764356	0,0274412077
58	0,0384727463	0,0331773711	0,0286108494
59	0,039947171	0,0345077952	0,0298090678
60	0,0414518916	0,0358678596	0,0310360589
61	0,0429870102	0,0372577141	0,0322920169
62	0,0445526273	0,0386775068	0,0335771338
63	0,0461488424	0,0401273841	0,0348916
64	0,0477757536	0,0416074907	0,036235604
65	0,0494334576	0,0431179699	0,0376093323
66	0,0511220501	0,0446589632	0,0390129699
67	0,0528416255	0,0462306108	0,0404467
68	0,0545922773	0,0478330511	0,0419107041
69	0,0563740976	0,0494664215	0,0434051623
70	0,0581871775	0,0511308576	0,0449302529
71	0,0600316071	0,0528264938	0,0464861526
72	0,0619074756	0,0545534633	0,0480730369
73	0,0638148709	0,0563118977	0,0496910795
74	0,0657538803	0,0581019275	0,0513404528
75	0,0677245897	0,059923682	0,0530213278
76	0,0697270844	0,0617772892	0,054733874
77	0,0717614488	0,0636628758	0,0564782599
78	0,0738277663	0,0655805676	0,0582546522
79	0,0759261195	0,0675304891	0,0600632165
80	0,07805659	0,0695127636	0,0619041174

Little theory about 3d crosstalk

When you are viewing picture for your left eye, the patch stripe consists of two pictures, the left eye patch and the black portion of the right side picture.The black is not completely black and it depends of televisions contrast ratio. In calculations we normalize the luminance that complete black is 0 and full white is 1. There is no complete black ( unless you have OLED) so in our calculations black is the contrast ratio CR. If my tv has CR 1:3000 then luminance of black will be 1/3000.

We'll call 3d crosstalk contrast as 3dCR.

The patch luminance of "right" picture will be ( CR + power(patch,gamma) *(1-CR)) because the patch number has to be transformed to linear values through gamma power function and then it has to fit between values CR and 1. The luminance of "wrong" picture will be black multilpied by 3dCR.
Then the luminance of the patch you selected is:
( CR + power(patch,gamma) *(1-CR)) + CR*3dCR

The white stripe ( the "wrong" picture ) consists of black of "right" picture and white of "wrong" picture multiplied by 3dCR.
Then the white stripe luminance is: CR + 1 * 3dCR

Because you selected the patch that equals the white stripe:
( CR + power(patch,gamma) *(1-CR)) + CR*3dCR = CR + 1 * 3dCR

I'll then solve 3dCR:
( CR + power(patch,gamma) *(1-CR)) + CR*3dCR = CR + 1 * 3dCR
CR + power(patch,gamma) *(1-CR) + CR*3dCR = CR + 1 * 3dCR
power(patch,gamma) *(1-CR) + CR*3dCR = 1 * 3dCR
power(patch,gamma) *(1-CR) = 1 * 3dCR - CR*3dCR
power(patch,gamma) *(1-CR) = 3dCR * (1 - CR)
power(patch,gamma) = 3dCR
The equation seemed difficult at first but in the end only the patch luminance is needed for 3d contrast ratio!

I've precalculated 3d contrast ratio ( = 1/3dCR) values for different gamma values:

Patch	2,2	2,3	2,4
0	infinite	infinite	infinite
1	196 965	342 801	596 618
2	42 867	69 610	113 038
3	17 568	27 395	42 717
4	9 329	14 135	21 417
5	5 710	8 461	12 536
6	3 823	5 563	8 093
7	2 724	3 902	5 591
8	2 030	2 870	4 058
9	1 567	2 189	3 059
10	1 243	1 718	2 375
11	1 008	1 380	1 890
12	832	1 130	1 533
13	698	940	1 265
14	593	792	1 059
15	509	676	898
16	442	583	769
17	387	507	665
18	341	445	579
19	303	393	509
20	270	349	450
21	243	312	400
22	219	280	358
23	199	253	322
24	181	229	291
25	166	209	263
26	152	191	240
27	140	175	219
28	129	161	201
29	119	148	184
30	111	137	170
31	103	127	157
32	96	118	146
33	90	110	135
34	84	103	126
35	79	96	117
36	74	90	110
37	70	85	103
38	66	80	96
39	62	75	91
40	59	71	85
41	56	67	80
42	53	63	76
43	50	60	72
44	48	57	68
45	45	54	64
46	43	51	61
47	41	49	58
48	39	47	55
49	38	44	52
50	36	42	50
51	34	41	48
52	33	39	45
53	32	37	43
54	30	36	41
55	29	34	40
56	28	33	38
57	27	31	36
58	26	30	35
59	25	29	34
60	24	28	32
61	23	27	31
62	22	26	30
63	22	25	29
64	21	24	28
65	20	23	27
66	20	22	26
67	19	22	25
68	18	21	24
69	18	20	23
70	17	20	22
71	17	19	22
72	16	18	21
73	16	18	20
74	15	17	19
75	15	17	19
76	14	16	18
77	14	16	18
78	14	15	17
79	13	15	17
80	13	14	16

So if I have selected patch number 37 for blue color and my gamma is 2.4, the 3d contrast ratio for blue is 1:103 which means less that 1% of blue crosstalk. The table also shows why knowing your gamma setting is important.

You can calculate your white 3d contrast with this formula:

The white contrast = (

( Red contrast * 0,212655 ) +

( Green contrast * 0,715158 ) +

( Blue contrast * 0,072187 )

)

The white contrast = (
( Red contrast * 0,212655 ) +
( Green contrast * 0,715158 ) +
( Blue contrast * 0,072187 )
)

The test pictures with 60 patches: