Image, sensors, detail, resolution, etc…

How much detail has your camera? 14 megapixels, 7, 1.5? What is detail? Resolution?

At present there are 2 types of sensors, the Bayer array (Colour Filter Array, CFA) and the Foveon. Bayer sensors cannot “see” less than their combined GRGB unit array which I will call “unit lens”. A unit lens for a Canon 1DS Mk III is a square (2x2) twice the pixel pitch i.e. 12.8µm. This might look surprising but you can try it yourself by using bigger “unit lenses” made of 3x3 (9 pixels) or a 4x4 (16 pixels). Although the final output would be still the original “MP” count the resulting image would have much less detail. I am sure some of the readers can come up with examples to back up this.

In the Foveon sensor the pixel pitch coincides with the “unit lens”. At a first glance it appears that a Sigma has more detail than a Canon 1DS MK III. However the Canon is a full frame sensor and has a lot more unit lenses than the Sigma. But if you crop the image of a Canon 1DS MK III to the size of a Sigma (1.7 factor, around 11 megapixels) the Sigma will have more detail.

On average a Bayer sensor will not deliver more than its flat number of unit lenses multiplied by √2 (square root of 2, 1.4142...) meaning it will not resolve more than the combined diagonal of a single pixel. A Canon 1DS MK III will have no more than 5,656,854 accurate readings. You may say “This is ridiculous. I have an image with 16 million pixels all the time with no noise!” Yes, you may have it but the image has been up—rezzed in camera; even if it looks pleasant to the eye it is still inaccurate. 

In the real world this means that if you put a Macro 1:1 lens in front of a camera you can only detect textures/points as the Minimum Detail Perceived or MDP. There is another element to be taken into account, noise, which is linked to pixel pitch. If you increase pixel pitch to reduce noise your images will become increasingly soft. If you decrease pixel pitch your images will start getting noisy and colour inaccurate.

Camera	Pix pitch (µm)	Pix Pitch x √2 (µm)	Nf	MDP (µm)
Canon 1DS III	6.4	9.05	0.80	11.31
Canon 60D	4.3	6,09	0.64	9.51
Canon 500D	4.69	6.63	0.68	9.75
Canon G12	2.08	2.94	0.20	14.70
Nikon D3X	5.93	8.38	0.77	10.88
Nikon D7000	4.69	6.63	0.68	9.75
Nikon D3S	8.46	11.96	0.92	13.00
Olympus E5	4.29	6.06	0.64	9.46
HBlad H3DII-39	6.80	9.61	0.82	11.72
HB H3DII-39 MS	6.80	9.61	0.82	11.72
HBlad H3DII-50	6.01	8.49	0.78	10.88
HBH3DII-50 MS	6.01	8.49	0.78	10.88
Leaf Aptus II 10	6.01	8.49	0.78	10.88
Leaf Aptus II 12	5.20	7.35	0.72	10.20
Sigma SD9	9.12	9.12	0.98	9.31
Sigma SD15	7.84	7.84	0.88	8.90
Sigma SD1	5.00	5.00	0.70	7.14

The table above shows that most cameras on a 1:1 capture approximately the same detail in the region of “fine” to “very fine” silt as described in this table 

http://pubs.usgs.gov/of/2000/of00-358/graphics/chapter1/c1f9chrt.gif

You can test this with any camera by knowing what is your fixed lens or zoom macro ratio and shoot textures, sand, clay, silt, foliage at will. Bayer sensors will never deliver less than their pixel pitch multiplied by √2. Anything below those values will look “mushy”. 

The DSLR that is able to capture more detail (on paper at least) is the SD1. 

The Bayer sensor has an advantage in what concerns noise. As it is planar there is an almost even error distribution throughout the coloured pixels. This means that, although Red photons can hit and be counted at Green and Blue pixels, the same happens to Green and Blue photons. The mistaken readings tend to cancel each other when counting. It does not matter if 20 Red photons were counted on the Blue pixel if 20 Blue photons were also counted on the Red pixel. Unfortunately the Foveon sensor, due to its geometry, does not benefit of this cancellation effect. However there is no up—rezzing process in camera and each pixel is a pixel.

What is the ideal pixel pitch?

Pixel pitch optimization is a function of its length, against noise. The curve for pixel pitch is similar to a Gaussian (aka Bell Curve) where the x coordinate is length and y is a multiplying scalar factor. The curve is truncated i.e. =0 for values of x<≤0.7µm. µ is around 9.5µm and σ is a value where the function will be 0.4 when x=3µm. This Gaussian function (pixel pitch noise factor or Nf) may be used to further ascertain how accurate your sensor is.

A Detail formula looks like:

P_d = 10 log (T_c x N_f)

Where

Pd= Photographic detail

Tc = True count

Nf = Noise factor

The above formula gives its results in decibels. Some calculations below:

Camera	Mega”pixels”	Pix pitch (µm)	True count	Noise factor	Exact Readings	Px Detail
Canon 1DS III	21,026,304	6.4	7,433,921	0.80	5,947,136	68,712
Canon 60D	17,915,904	4.3	6,334,228	0.64	4,053,905	66.079
Canon 500D	15,054,336	4.69	5,322,511	0.68	3,619,307	65.559
Canon G12	9,980,928	2.08	3,528,790	0.20	705,758	58.487
Nikon D3X	24,385,536	5.93	8,621,589	0.77	6,638,624	69.356
Nikon D7000	16,084,992	4.69	5,686,903	0.68	3,867,094	65.873
Nikon D3S	12,052,992	8.46	4,261,376	0.92	3,920,465	65.93
Olympus E5	12,192,768	4.29	4,310,794	0.64	2,758,908	64.41
HBlad H3DII-39	39,031,344	6.80	13,799,664	0.82	11,315,724	70.539
HB H3DII-39 MS	39,031,344	6.80	39,031,344	0.82	32,005,702	75.052
HBlad H3DII-50	50,135,232	6.01	17,725,481	0.78	13,825,875	71.407
HBH3DII-50 MS	50,135,232	6.01	50,135,232	0.78	39,105,481	75.922
Leaf Aptus II 10	55,728,000	6.01	19,702,823	0.78	15,368,202	71.866
Leaf Aptus II 12	80,000,640	5.20	28,284,496	0.72	20,364,838	73.089
Nikon and Sony have equivalent sensors ie, Nikon D3X = Sony A900
	Megapixels
Sigma SD9	3,429,216	9.12	3,429,216	0.98	3,360,631	65.264
Sigma SD14	4,646,400	7.84	4646,400	0.88	4,088,832	66.116
Sigma SD1	15,360,000	5.00	15,360,000	0.70	10,752,000	70.315

Conclusion

If you are comparing Dynamic Range there is hardly any difference between most of the cameras listed above; just a matter of brand loyalty, personal taste and efficient marketing. Dynamic Range is the Column Px detail divided by 6. The Canon G12 scores the lowest with 9.6 stops and the Hasselblad H3DII-50 MS with 12.5 stops. These results are consistent, the Leaf Aptus II 10 claims having 12 stops of Dynamic Range ie 72dB (here 71,886). Some website tests show that the majority of DSLRs has a DR of around 9 stops (54 dB only). It appears to me that their engineers are not making the best of what they have available or the simple presence of a AA filter is enough to take away 12dB (2 stops).

The main difference on the results is the brute numbers of Exact Readings. The Hasselblad H3D-50 Multi Shot can deliver a staggering 39 million correct readings against the pauper Canon G12 with just 706,000 a stupendous factor of 56!!! I just wonder what most Point & Shoots are really showing of reality. A curiosity… a Canon G12 sells for $500. If you multiply by 56 you get $28,000 close to the price of the Hasselblad. Is the industry following this type of table as a standard to set their prices?