Pixels on the Object

Magnification and closest focusThe object fills at most 90% of the frame, unless the equipment cannot get that close. The limit is the maker’s maximum magnification at the closest focus, for each combination: the lens alone from its specification; with Fujifilm’s tubes from Fujifilm’s table, which also gives the distance and the free space in front of the lens; with an extender from the maker’s figures for that lens (OM System) or its stated rule (Fujifilm: magnification times the factor, focus as the lens’s own). Extenders appear only with lenses their maker lists as compatible; tube and extender are not combined. A lens that cannot focus far, such as Laowa’s 2.5–5×, starts at its own smallest magnification, as a lens behind a tube does.

Adapters and crop modesNikon F lenses go on Z bodies through Nikon’s FTZ II, which holds the lens at its own distance and adds no glass: magnification and closest focus are the lens’s own. An APS-C lens on a full-frame body runs the body in its crop mode — DX on Nikon, APS-C on Sony and Canon — with only the pixels inside that area.

Tubes without a tableKenko publishes no magnification for its rings. The tool takes the focal length each lens works at when it is closest, from its own closest focus and magnification, and adds the ring to it by the thin-lens model. Against Fujifilm’s table the same estimate comes out between 11% low and 1% high in magnification, within 3% in distance. Behind a tube the lens cannot focus far: at infinity it gives tube ÷ focal length, which sets the largest object it frames.

Pixels on the objectpixels per mm = magnification ÷ pixel pitch, over the object’s length and width; an oval for a round outline; ppi = pixels per mm × 25.4.

PHOTARCH’s levelsRecord shot from 4 pixels per millimetre on the object (about 102 ppi); Study from 12 (about 305 ppi), with at least 10 bits recorded; Reproduction from 24 (about 610 ppi), with at least 12. A level needs both its pixels and its bits; under 4 pixels per millimetre the equipment gives less than a record shot. The bits are the ones the camera records in a raw, as its maker states them. A later iPhone is taken to record at least the bits of an earlier one that was measured. Where nothing is known, the bits are not held against the level, and the tool says so.

Distance and scale errorSensor to object by the thin-lens model, pulled to the published closest-focus distance at the combination’s maximum magnification. Closest focus is counted from the sensor where the maker says so: Fujifilm, Nikon and Hasselblad state it, Sony and Canon define it so in general; OM System and Apple do not say. A part this high above the ground measures too large by height ÷ (distance − height) when the scale is taken from the ground.

Diffraction and depth of fieldThe effective aperture is f-number × (1 + magnification), the f-number including any extender. Diffraction’s blur spot is 2.44 × 0.55 µm × effective aperture, given in pixels: up to two it costs little; from about five, its cut-off falls below what the pixels can record and nothing finer than a pixel is left. Then the detail stops at 2 × magnification ÷ (0.55 µm × effective aperture) pixels per millimetre on the object, however many pixels there are. Depth of field is counted with a blur of two pixels.

Best for this objectEvery camera with every lens it takes, worked out for the object as set: the one that puts the most pixels on it. When its bits keep it below a level that another camera reaches on the object, the most at that level comes too. Recommendations name a camera and a lens only, never a tube or an extender; those can be set by hand and compared. Within 1%, your own equipment goes first, then your camera with another lens; other bodies that give the same are named.

The recommendationEvery camera in the list with every lens it takes is worked out for this object, without tubes or extenders. Your own camera’s best comes first, when it puts more than 10% more pixels on the object; then the most any other camera gives, when that is 10% more again; then the highest PHOTARCH level — by the pixels on the object, held to the bits the camera records — when it is higher than all of those, even at fewer pixels. Within 1% of each other, published figures go before estimates.

LimitsReal lenses differ from the thin-lens model, more so with tubes. Pixels are not detail: the lens, the light and the focus decide how much of the sampling is real.