So how accurate is the lens magnification and depth of field calculator? In the following, results for some popular lenses are compared to the figures published by the manufacturers.

lens type | MFD | extension tube | |||||
---|---|---|---|---|---|---|---|

none | 12 mm | 25 mm | |||||

magnification | |||||||

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 standard (i.e. 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 photographic lens can be treated as a simple thin lens is thus working surprisingly well.

The reference values were published by Canon [2003].

lens type | MFD | magnification | comments | |
---|---|---|---|---|

data sheet | calc. | |||

Canon EF 100mm f/2.8L Macro IS USM | 0.30 m | 1.00 | 1.00 | focal length assumed as 75 mm |

Leica DG Macro-Elmarit 45 mm f/2.8 ASPH OIS | 0.15 m | 1.00 | 1.00 | focal length assumed as 37.5 mm |

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 |

Zeiss ZF Makro-Planar T* 50 mm f/2 | 0.230 m | 0.50 | 0.47 |

Again, the magnification calculator is pretty accurate. However, most of these macro lenses are seemingly violating the basic limitation that the minimum focusing distance must be at least 4 times the focal length, as derived in equation (M14). So what's wrong?

The answer is simply that they don't violate it—these lenses have an internal focusing mechanism that is changing the focal length during close-up, i.e. the focal length is slightly reduced. This effect is also accounted for by the calculator.

It seems most manufacturers don't publish depth of field tables of their lenses. The only exceptions I am aware of are the excellent technical data sheets from Leica and Zeiss. For validation of the depth of field calculator, two classic Leica lenses and one recent Zeiss lens of different focal lengths were selected [Leica 2013a, Leica 2013b, Zeiss 2015]. Note however that Leica does not publish the underlying circle of confusion which we also need to know for our calculator. Based on the Leica data, it was estimated as 0.033 mm. This happens to be identical to the value published by Zeiss.

lens type | f-stop | focusing 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 1.4 f/85 | 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 photographic lens can be modeled as a simple thin lens is working very well.