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Comparison of SNR (18%) across formats
Posted By: dosdan, 01-18-2011, 05:19 AM

It is worthwhile to data mine the treasure trove of DxOMark camera sensor data with the aim of getting a better understanding of the performance of different camera formats.

In this article I'll use the measured Signal-to-Noise (SNR) 18% performance. A 18% grey level is the accepted level in Photography & Videography of typical scene reflectance, so the SNR 18% indicates the level of mid-tone noise in a typical well-exposed shot.

Take an APS-C and a P&S camera. Assuming that the DSLR is an APS-C Nixon/Pentax/Sony (1.5x CF) and assuming that the P&S has a 1/2.5"-type sensor, the areas of the respective sensors are 370 mm2 and 24.7 mm2.

Image sensor size

The SNR improvement due to the bigger sensor when normalised to the same size output, e.g an 8"x10" print from both cameras, is the square root of this ratio i.e. root2(370/24.7) = 3.9 times less noise.
Expressed as dB, that's 20 log10(3.9) = 11.8 dB.
Expressed as stops, it's 2 log2(3.9) = 3.9 stops.

If it's a high-end P&S it will probably have a larger 1/1.7"-type sensor. The area of this sensor is 43.3 mm2.
SNR is root2( 370/43.3) = 2.9 times less noise.
20 log10(2.9) = 9.2 dB.
2 log2(2.9) = 3.1 stops.

When discussing SNR, 3 dB = 1 stop. The fact that ISO sensitivity can also be expressed in stops leads to an interesting result.

Say 4 sensors have SNRs @ ISO100 of:

A. 37 dB (noisest)
B. 38 dB
C. 39 dB
D. 40dB (best)

Since 3 dB SNR equals 1 stop, 1 dB = 1/3 stop. You can normalise these 4 sensors to an equivalent SNR:

A. 37 dB @ ISO100
B. 37 dB @ ISO125 (1/3 stop higher ISO)
C. 37 dB @ ISO160 (2/3 stop higher ISO)
D. 37 dB @ ISO200 (1 stop higher ISO)

So you can see that the best sensor in this group ("D") can be used at twice the ISO sensitivity as "A", and at 2/3 stop higher sensitivity than "B", for the same SNR. So knowing and understanding the 18% SNR value means you also know what higher ISO performance you are likely to be able to use.

To see how close theory matches reality, compare the DxOMark SNR 18% chart under the "Print" (output normalised) tab for the Pentax K-5 1.5x CF DSLR with a Canon G10 1/1.7"-type P&S:

DxOMark - Compare sensors

The measured SNR values at manufacturer's ISO 100 are
K-5: 40.8 dB @ actual ISO91
G10: 31.3 dB @ actual ISO117

To normalise these to the same ISO, the correction is 10 log10(91/117) = – 1.1 dB i.e. this should be subtracted from the ISO91 value to match a ISO117 value:

40.8 dB – 1.1 dB = 39.7 dB.

The corrected difference between the two sensors is thus:

39.7 dB – 31.3 dB = 8.4 dB (2.8 stops) compared to the theoretical 9.2 dB, so the Canon sensor is a little better for its size than predicted.

Repeating the exercise for the same Sony sensor as used in the K-5, but this time using the Nikon D7000 and adjusting its 41.1 dB SNR 18% @ actual ISO83 to match ISO117:

39.6 dB – 31 dB = 8.6 dB difference. So the DxOMark Sony APS-C figures for the K-5 & D7000 show good consistency.

Corrected true ISO200 SNR 18% figures for other recent sensors of various crop factors are shown below. I chose ISO200 because some cameras don't go to ISO100. (To convert ISO200 values to ISO100 values, add 3 dB.) The difference in stops relative to the D3100 is also shown. This camera was chosen as the reference as it is in about the middle of the APS-C pack in terms of 18% SNR performance.

TABLE 1

Camera CF Corr. SNR Stops SNR rel. D3100
645D 0.78 41.7 1.9
D3s 1 41.5 1.9
D3 1 40.6 1.6
D700 1 40.3 1.5
D3x 1 40.1 1.4
5DII 1 39.3 1.1
A900 1 38.9 1.0
A850 1 38.5 0.9
1DIV 1.3 38.0 0.7
5D 1 37.9 0.7
K5 1.5 37.5 0.5
D7000 1.5 37.4 0.5
D90 1.5 37.0 0.4
D5000 1.5 36.9 0.3
A700 1.5 36.4 0.2
Kx 1.5 36.1 0.1
50D 1.6 36.1 0.1
A550 1.5 36.0 0.0
SLT A55 1.5 35.9 0.0
60D 1.6 35.9 0.0
D3100 1.5 35.9 0.0
Kr 1.5 35.8 0.0
D300s 1.5 35.8 0.0
550D 1.6 35.8 0.0
K20D 1.5 35.5 -0.1
D300 1.5 35.4 -0.2
1000D 1.6 35.3 -0.2
40D 1.6 35.3 -0.2
A390 1.5 35.2 -0.2
GH2 2 35.1 -0.3
7D 1.6 34.9 -0.3
NX100 1.5 34.6 -0.4
K7 1.5 34.6 -0.4
PEN EPM1 2 34.4 -0.4
G2 2 34.3 -0.5
E620 2 34.2 -0.6
PEN EP2 2 34.1 -0.6
E5 2 33.8 -0.7
GF1 2 33.7 -0.7
S90 4.5 29.5 -2.2
G12 4.5 29.0 -2.3
S95 4.5 28.8 -2.4
P7000 4.5 28.7 -2.4
LX5 4.3 28.6 -2.4

You can see the APS-C group (CF 1.5x-1.6x) has about 1 stop total variation in SNR 18% (and hence ISO) performance with the K-5/D7000 currently at the top.

Consider the D3100 & the G12. The difference in SNR 18% is 2.3 stops. This means that the SNR should be about the same for both of them with the D3100 @ ISO500 & the G12 @ ISO100 since ISO100-> ISO200 (1 stop) -> ISO400 (2 stops) -> ISO500 (2 & 1/3 stops). Since the 1/2.5" (cheapie; CF 6x) & 1/1.7" (high-end; CF 4.5x) P&S sensor sizes are currently the most common, this means a P&S will be approximately 2.5 stops (high-end) to 3.5 stops (cheapie) inferior to a DSLR in ISO performance.

Note: older P&S had even smaller sensor areas, so the improvement of upgrading to a DSLR will be greater.


Dan.

Last edited by dosdan; 12-22-2011 at 04:36 PM.
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01-19-2011, 12:47 AM   #2
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Here's the theoretical SNR difference between digital camera formats. I've used APS-C as the SNR reference rather than FF, because it is the most popular DSLR format.

TABLE 2
Format CF SNR dB SNR Stops
645D 0.79 5.7 1.9
FF 1 3.6 1.2
APS-H 1.26 1.6 0.5
APS-C 1.52 0.0 0.0
APS-C (Canon) 1.6 -0.4 -0.1
Four-Thirds 2 -2.4 -0.8
CX 2.72 -5.1 -1.7
1/1.6" 4.3 -9.0 -3.0
1/1.7" 4.55 -9.5 -3.2
1/2.5" 6.02 -12.0 -4.0

Dan.

Last edited by dosdan; 10-08-2011 at 01:41 PM.
01-21-2011, 08:52 PM   #3
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Since publishing Table 2, it been nagging at me that, while Table 1 is good for interpreting relative SNR performance differences, the reference point of the Nikon D3100 was not that appropriate if I wanted to examine the performance both within and between each format compared to the best technological performance possible. In the formats covered here the leader is the Canon S90 in the 1/1.17" class. (I'm using DxOMark so I'm limited to the cameras that can produce a raw output file & which DxO has tested, which is a pity as I'd love to see the SNR performance of the 1/2.3" Back-Side Illumination sensor in the Canon SD 4000 IS/IXUS 300 HS.) The reasons that the P&S cameras seem to have the best sensor technology for their relative sensor size are due to the size of the market, the fierce competition and the short product cycles.

Table 2 shows that a 1/1.7" sensor, based on relative sensor areas, should theoretically be 3.164 stops inferior in SNR to a APS-C sensor. With my D3100 reference point, the difference was only 2.2 stops. I therefore renormalised to a 39 dB SNR point which placed the S90 in the correct position for its format (29.5 dB/-3.164 stops).

Once re-normalisation was performed, I then grouped the results together by format and applied offsets derived from the unrounded stops in Table 2 to account for the difference in sensor sizes. The objective is to compare the SNR performance (and hence the level of sensor technology) between classes. The result is below.

TABLE 3
Format Stops (format compared to S90 in 1/1.7")
MF 
645D -1.0
FF
D3s -0.4
D3 -0.7
D700 -0.8
D3x -0.8
5D II -1.1
1D3s III -1.2
A900 -1.2
A850 -1.4
5D -1.6
APS-H
1D IV -0.9
1D3 III -1.3
APS-C
K5 -0.5
D7000 -0.5
A580 -0.6
D90 -0.7
D5000 -0.7
A700 -0.9
NEX-3 -0.9
Kx -1.0
A560 -1.0
A550 -1.0
SLT A55 -1.0
D3100 -1.0
Kr -1.1
D300s -1.1
K20D -1.2
D300 -1.2
A390 -1.3
NX100 -1.5
K7 -1.5
 
APS-C (Canon)
50D -0.8
60D -0.9
600D -0.9
550D -0.9
1100D -1.1
1000D -1.1
40D -1.1
7D -1.2
Four-Thirds
GH1 -0.5
GH2 -0.5
PEN EPM1 -0.7
G2 -0.7
E620 -0.8
PEN EP2 -0.8
E5 -0.9
GF1 -1.0
 
CX  
J1 -0.5
 
1/1.6"
LX5 -0.5
LX3 -1.1
1/1.7"
S90 0.0
G11 0.0
G12 -0.2
S95 -0.2
P7000 -0.3


Dan

Last edited by dosdan; 09-06-2012 at 11:26 PM.
10-08-2011, 01:37 PM   #4
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Tables 2 & 3 have been updated to include the new Nikon CX format

Dan.

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