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Macro DOF and Trade of with Cropping
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Continuous Light Exposures on a Tripod
Handheld Continuous Light Exposure
This section explores the advantage in depth of field by shooting a subject at lower magnification and cropping to achieve the desired composition compared to shooting with close to the final composition and not cropping significantly.
The equations for macro depth of field are defined in the Macro DOF section. On this page it is assumed throughout that the lens is normally mounted in the forward direction.
If the uncropped magnification is M1 and the lower magnification used is M2 the effective crop magnification will be Mc=M1/M2 to arrive at the same overall subject size. The total overall image resolution and sharpness will probably be lower but it will be easier to obtain DOF in the cropped case.
In order to calculate this, the size of the circle of confusion needs to also be scaled for the cropped case, so if the uncropped circle of confusion is C1 then C2=C1/Mc to have the same sharpness criteria. This assumes that both exposures are above the diffraction limit.
There will be less light loss at lower magnifications so a smaller aperture would need to be set to achieve the same exposure. f2=f1*(M2/P2+1)/(M1/P1+1) where P1 and P2 are the lens pupilary magnifications at the uncropped and cropped magnifications respectively. For overall linear extension focusing the pupilary magnification will be constant so P1=P2, however for other focus methods, in particular internal focus the pupilary magnification can be expected to change.
Additionally, for exposure limited handheld cases the shutter speed will need to be increased (made shorter) by the factor Mc to limit camera shake. So in this case f2=f1*(M2/P2+1)/(M1/P1+1)/sqrt(Mc).
So the following table details the situations where this technique may be applicable:
|Exposure Type||Exposure Limit: Cropped Shot Action||Exposure Unlimited: f-stop Limit|
|Continuous Light on a Tripod||Subject movement may force a lower limit on shutter speed: Adjust f-stop to take advantage of reduced magnification light loss up to the diffraction limit.||No subject movement: f-stop limited by the diffraction limit.|
|Continuous Light Handheld||Camera shake may force a lower limit on shutter speed: Increase shutter speed to compensate for crop magnification and adjust f-stop for the balance of magnification light loss up to the diffraction limit.||Unlikely to be the case|
|Flash||Flash may have limited power: Adjust f-stop to take advantage of reduced magnification light loss up to the diffraction limit.||Plenty of flash power: f-stop limited by the diffraction limit.|
Calculating the ratio of the cropped to uncropped depth of field for a typical telephoto lens with a pupilary magnification of 2 and compensating the set aperture for the magnification light loss results in the following plot.
So we can see from this that the increase in DOF is proportional to the crop magnification Mc. This be the same regardless of the pupilary magnification P as the f-stop change effectively compensates for P.
The following plots show the required change in f-stop number for pupilary magnification P values of 0.5 (retrofocus lens), 1 (standard lens), 2 (telephoto lens) and non-constant models of P based on measured values for the EF 100mm f2.8 Macro USM and MP-E 65mm f2.8 1-5X MacroPhoto. NB the light stop at the front of the MP-E 65mm makes it difficult to measure the pupilary magnification accurately in the 1:1 to 3:1 range.
This type of operation is likely for continuous lighting with the camera mounted on a tripod where the shutter speed needs to be maintained to freeze subject movement. The diffraction limit will stop the photographer stopping down further in the uncropped case if there is no limit on shutter speed, so this approach will only be useful where the uncropped DOF is limited by exposure considerations.
In the case of handheld use the shutter speed will need to be increased in line with the crop magnification to mitigate camera shake, this will absorb most or possibly more than the available f-stop adjustment.
Thus the ratio of the cropped to uncropped depth of field for a typical telephoto lens with a pupilary magnification of 2, and compensating the set aperture for the magnification light loss after raising the shutter speed to keep camera shake controlled, results in the following plot.
Again this will the same for all pupilary magnifications and is equal to the square root of the crop magnification Mc.
The following plots show the required change in f-stop after allowing for the shutter speed increase.
So we can see here the photographer may need to open then lens up rather than stop down for the cropped exposure case depending on the prevailing uncropped magnification and the lens pupilary magnification chanracteristic.
In a real life situation the photographer will probably set a constant f-stop for reasonable sharpness and DOF and not have time to figure the change in f-stop in cropped exposures. This is most like to be the case for flash exposure.
So the below plots show the depth of field ratio with a fixed set f-stop, again for the same pupilary magnification cases.
We can see that operating this way still produces an advantage but is likely to result in diminishing returns at higher magnification. For a lens such as the MP-E 65mm the advantage is minimal.
Last Updated 05/06/2008
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