How to calculate focal reducer crop factor for APS-C to MFT?

Question

As far as I can tell, the crop factor determines the size of the projected image circle and should match the ratio of sensor diameters (with standard mount forward / backward distance).

My calculations have to be wrong, since the Metabones speed booster crop factors don't match the intended conversions. The 0.64x crop should cover the ratio MFT/FF (~0.5x), but the 0.71x shouldn't cover the ratio MFT/APSC (~0.83x Canon/0.76x Sony)

• MFT 21.6mm, APS-C 26.8mm(Canon)/28.2, FF 43.3mm
• Metabones XL 0.64x EF to MFT is for FF
• Metabones Ultra 0.71x EF to MFT is for APS-C

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Why don't my ratios add up? How do you properly calculate the focal reduction crop factor?

Answer 1

Metabones Ultra 0.71x EF to MFT is for APS-C

This is sort of incorrect.

Both the Metabones XL 0.64x EF to MFT and the Metabones Ultra 0.71x EF to MFT are primarily intended to be used with full frame EF lenses. If one reads the official Metabones product page for the Ultra 0.71x EF to MFT, one sees that there are several caveats to using an APS-C lens with it, and that it is marginally usable for recording 16:9 video, but not necessarily 4:3 stills, with APS-C lenses.

Unmodified EF-S mount lenses will not physically attach to this adapter. Other "APS-C only" lenses in the EF mount will attach, but the other caveats regarding using lenses with an APS-C size image circle with this adapter remain valid.

The full name listed at B&H is the

T Speed Booster Ultra 0.71x Adapter for Canon Full-Frame EF-Mount Lens to Micro Four Thirds-Mount Camera.

Only FF Canon EF lenses or equivalent third party lenses will project an image circle large enough to cover the µ4/3 sensor when used with the Metabones Ultra 0.71x EF to MFT. It does not provide full sensor coverage with third party APS-C lenses in the Canon EF mount that only cast an APS-C size image circle.¹ The apparent reason Metabones "recommends" the Metabones Ultra 0.71x EF to MFT, rather than the Metabones XL 0.64x EF to MFT, for APS-C lenses is because the vignetting issues will be much less severe with the 0.71X focal reduction than with the 0.64X reduction. They still point out that there may be issues with image circle coverage using APS-C lenses with the EF mount.

Below are two notes of particular interest from the Metabones product page:

EF-S lenses require modification to fit or may remain incompatible even after modification (but third-party DX lenses can be used without modification)

Even if the EF-S lens is modified to fit the EF mount of the adapter, there may be mechanical clearance issues with some EF-S lenses that have rear elements that protrude further out the back of the lens flange than EF lenses do.

Some EF-S and DX lenses² may not have enough coverage of the entire image circle for stills after widening by 0.71x (but video will have enough coverage).

The video comment seems to assume one is shooting in 16:9 format and thus not using the extreme corners of the 4:3 aspect ratio sensor. With a 17.3 mm width, only the center 9.73 mm of the sensor's 13 mm height would be used for 16:9 video. The resulting 19.84 mm diagonal is very close to 26.9 x 0.71 = 19.1 mm.

You might also find the press release from Metabones announcing the Speed Booster ULTRA 0.71x M43 with Autofocus to be helpful. It uses the phrase "DX and APS-C format lenses" several times. It also says (bold and italics added):

However, the new ULTRA design makes very effective use of exotic materials at the furthest limit of glassmaking technology, and as a result is almost perfectly corrected for use with all fullframe SLR lenses regardless of aperture. The Speed Booster ULTRA m43 will also work extremely well with many DX and APS-C format lenses provided the image circle of the lens is large enough.

Here's the full lens compatibility statement further down in the press release:

Lens Compatibility: Any full-frame (36 mm x 24 mm format) SLR lens with the appropriate mount can be used. DX format lenses can be mounted but may result in vignetting when the full Micro Four Thirds format is used, depending on the lens. DX lenses are fully supported when used on the Panasonic GH4 in Cinema 4k mode, and will function without abnormal vignetting. Canon EF-S lenses are not supported, but third-party EF-mount APS-C lenses can be mounted and will have full electronic functionality.

Thus, it seems the Metabones Ultra 0.71x EF to MFT was never intended to be 100% compatible with APS-C only lenses.

26.9mm is the 'nominal' diagonal of a Canon APS-C image sensor, which can range from 26.63mm to 27.26mm depending on the exact APS-C sensor made by Canon. One would assume all of Canon's APS-C only EF-S lenses can cover their largest APS-C sensor with a 27.26mm diagonal.³ One might also assume, with a fairly high degree of certainty, that most third party 'APS-C only' lenses would as well, since the same designs are also offered in other mounts, such as Nikon F and Minolta/Sony A, for cameras with slightly larger APS-C sensors with diagonals closer to about 28.2mm.

It is also the case that most zoom lenses expand the image circle as they are zoomed to longer focal lengths. EF-S lenses must have an APS-C sized image circle at their widest focal length setting, but that image circle will expand when zoomed to longer focal lengths (if there's nothing physically blocking the light at the rear of the lens). This same concept is illustrated with the EF 8-15mm f/4 L Fisheye lens. At the widest setting, the image circle does not completely cover a FF sensor. In fact, the full image circle is contained within the rectangular sensor. Only at 14-15mm does the full sensor receive light projected by the lens.

The only Metabones adapter for EF-S lenses to MFT that will provide a large enough image circle to cover the complete µ4/3 sensor at all lens focal lengths and apertures is the T Smart Adapter for Canon EF or Canon EF-S Mount Lens to Micro Four Thirds-Mount, which does no focal reduction a/k/a Speedboosting.

_{¹ Third party APS-C lenses for Canon EOS cameras use the EF mount, rather than the EF-S mount, which is still protected by patent. The patent has expired on the EF mount introduced in 1987. Even though they don't cast an image circle large enough for FF sensors, they can be attached to FF EOS cameras.
² "DX lenses" is used here as a broad term to refer to any lens intended for use on APS-C cameras only. This should be self apparent, since the adapter's product page on which the statement appears is not a Nikon F-mount adapter.
³ The 22.7 x 15.1 mm sensor with a calculated diagonal of 27.26 mm was used both in the original 10D, released before EF-S lenses were introduced, and in the EOS Digital Rebel/300D that was the first EOS camera with an EF-S mount flange with the extra slot needed to accommodate the extra tab on the lens bayonet. Unmodified EF-S lenses will not mate to the 10D in the same way they will not mate to any full frame Canon EOS camera. The Digital Rebel/300D was the first EOS camera with an EF-S flange on the front of the camera. The 10D was introduced in early 2003. The Digital Rebel/300D came out about six months later in the third quarter of 2003. The first EF-S lens was introduced simultaneously with the Digital Rebel/300D.}

Answer 2

Aspect ratio doesn't really matter for this particular purpose, because the corners of whatever rectangle you choose need to be covered by the image circle — so, the diameter needs to at least meet the a corner-to-corner distance.

If one were to crop a 36×24mm frame to 4:3, that'd be 32x24mm, and a smaller diagonal. But all of the real-world lenses are designed for the full format, so the smaller diagonal is irrelevant.

Note that the imaging area of a Micro Four Thirds sensor is 17.3×13mm, for a diagonal of 21.6mm, not 22.5 (citation). For Canon APS-C, it is 26.8mm. (Other brands use a marginally larger 28.2). And full-frame, of course, is 43.3mm.

If the Metabones adapter reduces the image circle by a factor of 0.64, APS-C lenses which really push the limits of the image circle may only cover a diagonal of 17.2mm, but full-frame lenses should cover 27.7mm (big enough for Canon APS-C). Or for 0.71×, 19.0mm and 30.8mm respectively.

So, generally, lenses designed for a full-frame image circle should be no problem with either of these adapters — 27.7 and 30.8 are both larger than 21.6. However, lenses designed to only cover APS-C might have shaded corners (17.2 and 19.0 are of course not larger).

But the thing is: the sensor diagonal only determines the minimum image circle. Lens designs are complicated, and it is often the case that the image circle projected by a given lens is considerably larger than the minimum required for the format. This is particularly true at larger focal lengths. See:

• Is there an easy way to tell the size of an image circle a lens has?
• Does the imaging circle size change when a lens zooms?

If you hoped to use wide-angle APS-C lenses, you might be out of luck. Others might or might not work. On the other hand, full frame lenses should generally be no problem at all. There's even room for quite a bit more extreme reduction than the adapters provide — I think this is what you mean with the "why not 0.52×?" question. It's likely that there are other practical problems making an adapter like that, but in terms of image circle it should be doable just fine.

For a practical example, look at this review of the Sigma 18-35mm f/1.8 DC HSM Art lens. This is designed for APS-C but will mount just fine on full frame, so it's a great visualization. The review includes comparisons at different focal lengths. At 18mm, the circle is readily visible (choose "no hood"), but at 35mm, just the corners are shaded. But even at 18mm, if we shrink the sample image to 64%, the corners of a Fourth Thirds sensor just touch the visible vignetting. (That's not pictured in the review, but it's easy to do in an image editing program — make a new layer with a box 48% as wide and 54% as tall as the original frame, in the center of the image. Then, shrink the original image layer by the strength of the focal reducer.) They're not even into the black. There are many situations where you might decide to live with that.

Answer 3

Crop factor --- The full frame 35mm film camera introduced in 1923 by Leitz Manufacturing and named Leica, became so popular that zillions of cameras using this format were marketed. The format dimensions or frame size measures 24mm height by 36mm long. The height to length ratio is 3:2, and this size enlargers exactly to film a 4x6 or 8x12 inch piece of paper. In other words, the length is 1.5xthe width. This format has gained the title “classic”. So many photographers have owned or used 35mm format cameras, there is an abundance of used but good lenses still available. Further, gray hairs like me are very familiar with how this format behaves when various focal length lenses are mounted.

As cameras evolved they shrunk mainly because technology advanced allowing reduced film sizes. As the century tuned, Kodak, introduced a 24mm wide film format. This was to be a new hybrid film camera system using film sandwiched with a transparent magnetic tape. The idea was, capture the image on film and store all manner of data on the tape. The format was called Advanced Photo System. Soon most all major camera makers jumped in to the fray. The typical frame size on the film is 16mm height by 24mm length called the APSC (C for classic format).

Because the APS-C format is 66% of the venerable 35mm format, the industry turned to the “crop factor” as an aid to help photographers choose focal lengths. To calculate the crop factor we divide the larger corner-to-corner measure by the smaller. The diagonal of the 35mm frame is 43mm. The diagonal of the APS-C frame is 28mm thus the crop factor is 43 ÷ 28 = 1.5 (values rounded). Gray hairs like me can divide their favorite preforming 35mm lens focal length by 1.5 to derive an equivalent focal length for the APS-C. This if I love a 105mm portrait lens on my 35mm the equivalent as to angle of view is 105 ÷ 1.5 = 70mm for the APS-C. This works every time.

The four thirds format measures 13.5mm height by 18mm length. The diagonal measure is 22.5mm. The crop factor is 43 ÷ 22.5 = 1.91 (OK to round to 2 or 50%). Thus the equal of a 105 portrait lens for the micro four third camera is 105 ÷ 2 = 50mm (OK to round). These work by shorting the focal length. Say a 50mm lens in combined with a 0.71 speed booster. Say a 50mm lens is set to 25mm working diameter (aperture). The f-# is 50 ÷ 25 = 2 (written as f/2). Now we mount a 0.71 booster. This combination reduces the focal length thus 50 x 0.71 = 35.5mm. Now the revised f=# is 35.5 ÷ 25 = 1.4. What happens is we gain 1 f-stop in speed.

You are equating “crop factor” with focal length alteration. The crop factor pertains to the ratio of the camera’s format size as comparted to the venerable 35mm full frame. One can make a loose connection between the magnification factor of an add-on lens but, I think this only complicates as it add no clarity.

Answer 4

As far as I can tell, the crop factor determines the size of the projected image circle and should match the ratio of sensor diameters (with standard mount forward / backward distance).

My calculations have to be wrong, since the Metabones speed booster crop factors don't match the intended conversions. The 0.64x crop should cover the ratio MFT/FF (~0.5x), but the 0.71x shouldn't cover the ratio MFT/APSC (~0.83x Canon/0.76x Sony)

I think your definitions instead have different meaning. Crop factor is Not about the lens. It merely specifies the size of your sensor (inversely relative to full frame size, i.e., 35 mm film size), and therefore describes the view that the sensor crops from the projected lens image. If your crop factor is 1.5x, it means that full frame is 1.5x larger dimensions (and your sensor is 1/1.5 or 0.67x dimension of the full frame 1x size). This is the total numerical meaning.

This sensor size is NOT about what the lens does, but it is about the cropped view that is captured on the cropped sensor, i.e., it does affect the resulting sensor image seen, but it is Not about what the lens does. DSLR cameras might use the exact same lens on different DSLR sensor sizes. i.e., different crop factors. If your camera sensor has a crop factor of 1.5x, it is 1.5x regardless of which lens you might mount on it.

Effective Focal Length due to Crop Factor is NOT about YOUR lens, it is about the lens that would be required on an uncropped 1x sensor that would then see the same view as your cropped sensor sees.

Crop factor is about sensor size, which then is about the captured field of view size.

The converter 0.7x number is Not crop factor, it is a multiplier of your sensor crop factor. It contains glass elements which do enlarge or reduce the image from the lens, so it does in fact modify the image size projected on the sensor. The sensor size captures what it can of it.

Example: A 1.5x crop factor sensor using a 0.7x converter has new effective crop factor of 1.5 x 0.7 = 1.05x (just meaning, when used, it makes a 1.5x sensor see about a 1x full size uncropped view).