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| Jean-Louis Ecochard | profile | all galleries >> Techniques & Tools >> Technical Talk about the 7D | tree view | thumbnails | slideshow |
Here is some technical talk about the Maxxum/Dynax 7D
The Konica Minolta 7D camera has a CCD sensor of 23.5 x 15.7mm
NORMAL LENS
A "normal" lens is a lens whose focal lengh is closest to the diagonal of the sensor.
The diagonal of the 7D sensor is 28.2 mm which means the "normal" lens for the 7D is a 28mm
RATIO TO 35mm
A 35mm film is 36 x 24 mm which is 2.3 times bigger in surface.
The diagonal of 35mm film is 43.2mm which is 1.53 times bigger than the diagonal of the 7D sensor.
That means that any lens that covers the 35mm sensor will appear 1.53 times enlarged when it covers the 7D sensor.
For KM lenses we have:
35mm Lens 7D 16mm 24mm 20mm 31mm 24mm 37mm 28mm 43mm 35mm 54mm 50mm 77mm 85mm 130mm 100mm 153mm 135mm 207mm 200mm 306mm 300mm 459mm 400mm 612mm 500mm 765mm 600mm 919mm
CIRCLE OF CONFUSION (CoC) Using the Zeiss formula (D/1730), where D is the diagonal of the sensor, the Circle of Confusion is 0.016 mm.
Kleptolux CoC Calculation
The “Circle Of Confusion” is typically calculated as the largest on-film circle that you see as a point on an 8x10” print when viewed it from a “normal” distance of about 1 ft (some say 2-3ft).
In my calculations I use the smallest two lines that a human eye can theoretically distiguish on an 8x10in print at a distance of 25cm. I use 25cm because it is the distance that Leica uses in the description of their R lenses. I use 8x10in because it is used in most CoC calculations. All these numbers are abitrary and I will show you the equations so that you can plug in your own numbers.
What is the resolution of the human eye?
Resolving power is the ability of an optical instrument to differentiate between two points or lines. The angle of resolution A of an optical instrument, based solely on the size of its aperture, is given by the formula: A = 0.02 x (L / D)
where A is the minimum separation angle in arc seconds (1 arc second = 1/3,600 degree), L is the wavelength of light in nanometers (1 nanometer =10-9meter), and D is the diameter of the aperture (e.g. the pupil of the eye) in centimeters.
The range of the human eye's resolution can be calculated theoritically using the diameter of the pupil (5mm) and the limits of the wavelengths of light the eye can see. The visible spectrum of the average human eye, extends from about 400 nm (blue) to 700 nm (red). Thus the limit of resolution of the human eye are:
0.02 x (700 / 0.5) = 28 arc second (red)
0.02 x (400 / 0.5) = 16 arc second (blue)
Note that 20/20 vision is often considered to be 1 arc minute and that is half of the maximum theoretical resolution for red.
So how many lines per millimeter can we see?
Trigonometry gives us the length of an image that can been seen at a certain distance given a viewing angle as: L = A x D
where L is the length of the image, A is the angle in Radians and D the distance from the image.
Thus we can calculate these lengths for our two resolution angles at 25cm from the print: L = (1/28) x (pi/180) x 250 (red)
L = (1/16) x (pi/180) x 250 (blue)
At 25cm from an image, you can observe details ranging in size from 0.155mm (red) to 0.273mm (blue). Since a line pair corresponds to two lines of this size, the theoretical corresponding spatial frequency of the eye (1/L/2)is between 3.21 line pairs/mm (red) and 1.83 line pairs/mm (blue).
Note that Leica uses 3 to 6 lines/mm at 25mm to calculate how big enlargements can be made.
The diagonal of an 8x10in print is 325mm which can be converted to ranging between 1,044 line pairs (red) and 596 line pairs (blue).
Calculating the CoC
The CoC formula is: D/L
where D is the diameter of the sensor and L is the number of possible resolvable lines on the diagonal of an 8x10in image (remember there are 2 lines per pair).
Thus kleptolux calculates that the CoC for the 7D for a single line varies between 0.014 mm (red) and 0.024 mm (blue) for an 8x10 print viewed at 25cm
or 0.027 to 0.047 mm for line pairs.
We can also calculate the CoC of 35mm film to vary between 0.021 and 0.036mm. This explains why the value of 0.030mm (i.e. midpoint) is often used as the CoC of 35mm film. KM uses 0.033mm for their lenses.
Note that the eye is most sensitive to 555nm light so the corresponding CoC would be 0.017mm (0.034mm for a line pair). If we use the Leica values of 3 lines/mm and 6 lines/mm we have CoC varying from 0.014mm to 0.021mm. If we use that 20/20 vision is 1 arc minute then we have a CoC of 0.013mm. Are you confused yet?
DIFFRACTION
Diffraction happens when the Airy circle is bigger than the CoC. The Airy circle depends on the f-stop and the wavelength of the light. The formula to calculate the size of the Airy disk is:
d = 2.43932 x lambda x f
d is the linear diameter of the first interspace (the middle of the dark zone that separates the Airy disk from the first ring), lambda is the wavelength of the light, f is the Focal Ratio of the lens.
F-Stop RED BLUE RED BLUE RED BLUE 555nm 555nm 555nm Airy Airy CoC CoC Diff. Diff. Airy CoC Diff 1 0.0017 0.0010 0.0135 0.0237 NO NO 0.0014 0.0171 NO 1.4 0.0024 0.0014 0.0135 0.0237 NO NO 0.0019 0.0171 NO 1.7 0.0029 0.0017 0.0135 0.0237 NO NO 0.0023 0.0171 NO 2 0.0034 0.0020 0.0135 0.0237 NO NO 0.0027 0.0171 NO 2.8 0.0048 0.0027 0.0135 0.0237 NO NO 0.0038 0.0171 NO 4 0.0068 0.0039 0.0135 0.0237 NO NO 0.0054 0.0171 NO 5.6 0.0096 0.0055 0.0135 0.0237 NO NO 0.0076 0.0171 NO 8 0.0137 0.0078 0.0135 0.0237 YES NO 0.0108 0.0171 NO 11 0.0188 0.0107 0.0135 0.0237 YES NO 0.0149 0.0171 NO 13 0.0222 0.0127 0.0135 0.0237 YES NO 0.0176 0.0171 YES 16 0.0273 0.0156 0.0135 0.0237 YES NO 0.0217 0.0171 YES 22 0.0376 0.0215 0.0135 0.0237 YES NO 0.0298 0.0171 YES 32 0.0546 0.0312 0.0135 0.0237 YES YES 0.0433 0.0171 YES 45 0.0768 0.0439 0.0135 0.0237 YES YES 0.0609 0.0171 YES 64 0.1093 0.0625 0.0135 0.0237 YES YES 0.0866 0.0171 YES
So on the 7D, using the kleptolux CoC, we have a theoretical diffraction throughout the entire visible spectrum at f/32. In practice it shows clearly at f/64 (see images below).
RESOLUTION
The Rayleigh criterion says that two points are resolved when the dark ring of one coincides with the center of the airy disk of the other, the corresponding resolution (in line pairs per mm) is:
R = 2 / (2.44 x W x F)
where F is the f-stop and W the light wavelength.
It gives us the following:
F-Stop Resolution for 555nm light (lines per mm) f/1 1,477 lp/mm f/1.4 1,055 lp/mm f/1.7 869 lp/mm f/2 738 lp/mm f/2.8 527 lp/mm f/4 369 lp/mm f/5.6 264 lp/mm f/8 185 lp/mm f/11 134 lp/mm f/13 114 lp/mm f/16 92 lp/mm f/22 67 lp/mm f/32 46 lp/mm f/45 33 lp/mm f/64 23 lp/mmThe width of the 7D sensor is 23.5mm and it has 3008 pixels covered by an RGBG Bayer pattern. It takes 2 pixels (e.g. RG or BG) to record true information so the sensor has an effective resolution of 32 lp/mm.
On the 7D, for a light of 555nm, you lose resolution after f/45.
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| Guest | 20-Aug-2008 13:47 | |
| Richard Chenevix Trench | 04-Oct-2007 13:49 | |
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