So how accurate is our calculator? In the following, results for some popular lenses are compared to the figures published by the manufacturers.
13.1.1 Non-macro lenses
For validation of the magnification calculator, a Canon instruction manual was used which lists the maximum magnifications for various lenses without lens extension tube, with a 12 mm lens extension tube, and with a 25 mm lens extension tube, respectively [Canon 2003]. MFD denotes the minimum focus distance of the lens.
|lens type||MFD||extension tube|
|none||12 mm||25 mm|
|data sheet||calc.||data sheet||calc.||data sheet||calc.|
|Canon EF 24 mm f/2.8||0.25 m*||0.16||0.12||0.64||0.62||1.22||1.16|
|Canon EF 28 mm f/1.8 USM||0.25 m*||0.18||0.15||0.61||0.58||1.13||1.04|
|Canon EF 35 mm f/2||0.25 m*||0.23||0.20||0.58||0.55||1.00||0.92|
|Canon EF 50 mm f/1.4 USM||0.45 m*||0.15||0.15||0.39||0.39||0.68||0.65|
|Canon EF 85 mm f/1.8 USM||0.85 m||0.13||0.13||0.27||0.27||0.44||0.42|
|Canon EF 135 mm f/2L USM||0.9 m||0.19||0.23||0.29||0.31||0.41||0.41|
|Canon EF 200 mm f/2.8L II USM||1.5 m||0.16||0.19||0.23||0.25||0.32||0.31|
*approximate value according to data sheet
For these non-macro lenses, the magnification calculator is pretty accurate, with a deviation below 10% (marked in green) or below 20% (marked in yellow) in most cases. The simplifying basic assumption that a camera lens can be treated as a simple thin lens is thus working surprisingly well.
13.1.2 Macro lenses
The following data were collected from the respective company websites.
|Canon RF 35 mm f/1.8 Macro IS STM||0.17 m||0.50*||0.41|
|Fujifilm Fujinon XF 60 mm f/2.4 R Macro||0.267 m||0.50||0.52|
|Leica Macro-Elmar-M 90 mm f/4 with Macro-Adapter-M||0.41 m||0.50||0.48|
|Lumix G Macro 30 mm f/2.8 ASPH Mega OIS||0.105 m||1.00||1.00||focal length assumed as 26.25 mm|
|Nikon AF-S Micro Nikkor 60 mm f/2.8G ED||0.185 m||1.00||1.00||focal length assumed as 46.25 mm|
|Olympus M.Zuiko Digital ED 60mm f/2.8 Macro||0.190 m||1.00||1.00||focal length assumed as 47.5 mm|
|Pentax smc DFA 50 mm f/2.8 Macro||0.195 m||1.00||1.00||focal length assumed as 48.75 mm|
|Sigma AF 105 mm f/2.8 EX DG Macro HSM OS||0.312 m||1.00||1.00||focal length assumed as 78 mm|
|Sony 50 mm f/2.8 Macro||0.200 m||1.00||1.00|
|Tamron SP 90 mm f/2.8 Di VC USD Macro||0.300 m||1.00||1.00||focal length assumed as 75 mm|
|Voigtländer 65 mm f/2 Macro Apo-Lanthar||0.31 m||0.50||0.43|
|Zeiss ZF Makro-Planar T* 50 mm f/2||0.230 m||0.50||0.47|
*approximate value according to company website
Again, the magnification calculator is pretty accurate. However, many of these macro lenses are seemingly violating the basic limitation that the minimum focus distance must be at least 4 times the focal length, as derived in equation (F10). So what’s wrong?
13.1.3 Focus breathing
The answer is simply that they don’t violate it—these lenses show an effect known as focus breathing, which refers to a change of focal length when the lens is focused. The nominal focal length applies for the lens focused at infinity, but may be shorter for small distances, i.e. the field of view gets wider. This effect is also accounted for by the calculator.
13.2 Depth of field
It seems most manufacturers don’t publish depth of field tables of their lenses. The only exceptions we are aware of are the excellent tech specs from Leica and Zeiss. For validation of the depth of field calculator, two classic Leica M lenses and one recent Zeiss lens of different focal lengths were selected [Leica 2013a, Leica 2013b, Zeiss 2015].
Note that Leica does not publish the underlying circle of confusion which we need to know for our calculator. Based on the Leica data, it was estimated as 0.033 mm (0.0013 inches). This also happens to be identical to the value published by Zeiss, and is therefore also used here.
|lens type||f-stop||focus distance||near limit||far limit|
|data sheet||calc.||data sheet||calc.|
|Leica Summilux-M 35 mm f/1.4 ASPH*||1.4||2 m||1.867 m||1.87 m||2.154 m||2.15 m|
|10 m||7.294 m||7.35 m||15.93 m||15.70 m|
|8||2 m||1.436 m||1.44 m||3.337 m||3.32 m|
|10 m||3.284 m||3.28 m||infinity||infinity|
|Leica Summilux-M 50 mm f/1.4 ASPH**||1.4||2 m||1.934 m||1.94 m||2.070 m||2.07 m|
|infinity||56.14 m||57.7 m||infinity||infinity|
|8||2 m||1.685 m||1.69 m||2.466 m||2.45 m|
|infinity||10.12 m||10.1 m||infinity||infinity|
|Zeiss Milvus 85 mm f/1.4||1.4||2 m||1.97 m||1.98 m||2.02 m||2.02 m|
|15 m||13.7 m||13.7 m||16.6 m||16.6 m|
|8||2 m||1.89 m||1.88 m||2.14 m||2.14 m|
|15 m||9.97 m||9.76 m||35 m||32.6 m|
*focal length 35.6 mm according to data sheet, **focal length 51.6 mm according to data sheet
The depth of field calculator shows an excellent agreement with the published figures. In many cases, the values are almost identical, with an error well below 10% even in the worst case. Again, the basic assumption that a camera lens can be modeled as a simple thin lens is working very well.