How Equivalent is Equivalent?

[Black Pearl]

I've been meaning to do this for ages but never got the time or the connections to gel.

People often talk about lens focal lengths giving the equivalent between cropped bodies and full frame bodies but there will always be the underlying fact that a particular lens will always be a particular lens and its characteristics will always be the same.

A 50mm is a 50mm no matter what. It might give the equivalent focal length of a 75mm on a (1,5x) crop camera but it will always be a 50mm. I know there are often (heated) arguments around this so I thought I'd have a bit of fun. As there are few 75mm lenses knocking about I went with a 35mm lens on a Nikon DX (1.5x crop) camera and a 50mm on a FX (FF) body.

Both shot from the same position, both shot with exactly the same settings:
Full manual mode: 1/40 sec; f/2.8; ISO 400
Both NEF files opened in Camera RAW 7.0 with all the settings synchronised. I aligned the layers and cropped the edges very slightly as the 35mm is the equivalent to 52.5mm not 50mm when multiplied by 1.5 to make the shots as close as possible.

Nikon D300s (12mp on a DX sensor) + 35mm:


Nikon D3 (12mp on a FX sensor) + 50mm:


As you can see the foreground/background separation between the two is significantly different even thought the equivalent field of views are the same. Another thing to note is the massive pixels on the D3 give a far nicer shadow rendering than the smaller ones on the D300s and though you can't see it there was far less noise visible when viewed at 100%.

As I said a bit of fun I've been meaning to do for ages.

If you want a nice shallow DoF for say portrait work - go FX
If you want loads of it for say landscape/macro - DX still has its place.

[RustBeltRaw]

This is a great little demo. Angle of views may match, but perspective doesn't change. Would be cool to see a transparent overlay of the photos to really highlight the differences.

If you want loads of it for say landscape/macro - DX still has its place.

I'd argue that a DX body will always be handy, especially for prime lens shooters. Easiest possible way to double your focal length options.

[klovibond]

Besides the extra cost of FF, as I'm primarily a wildlife tog I'll always welcome the extra reach I get from a crop sensor

[Colin Southern]

Besides the extra cost of FF, as I'm primarily a wildlife tog I'll always welcome the extra reach I get from a crop sensor

I always like to point out to people that although the FoV will always "zoom" with a crop-sensored camera, the actual amount of information captured depends on the pixel count of the two respective cameras. The 10.1MP Canon 1D3 (1.3x crop) and 21MP Canon Ds3 (FF) are probably good examples; on the face of it, the 1D3 may seem to have a 1.3x reach advantage, but when you do the math, one finds that a 1Ds3 image cropped to the same field of view actually contains around 30% more pixels.

You need a big difference in pixels to totally wipe out the reach advantage, but other more common scenarios can significantly reduce the advantage (eg an 18MP crop camera -v- a 36MP FF)

[KmH]

Note too that the person in the FX image sensor (D3) image is has slightly less scale in the image frame compared to the DX image.

[loosecanon]

err - looks like the exposure/development of the two images are different.

[RustBeltRaw]

err - looks like the exposure/development of the two images are different.

Remember that they were shot with two different cameras. Exposure and other qualities will vary slightly.

[Black Pearl]

err - looks like the exposure/development of the two images are different.

Err - nope.
Exactly the same settings on both bodies and I linked every setting ACR so the processing was identical. As I explained in the OP the D3 produced far softer shadows - we spotted it when comparing the images on the rear LCD's as the histogram looked different with more peaks on the left.

[rpcrowe]

The term "equivalent" to the best of my knowledge refers to the angle of view alone, not ancillary things like DOF, etc....

[Mike Buckley]

To change the subject a bit, I commonly see people recommending the use of a long focal length to "compress" the various elements in a distant landscape scene more than would happen using a short focal length. The corollary of your exercise is that the compression is the same whether using a long lens or cropping to the same field of view after using a short lens. This was proved to my satisfaction decades ago in a U.S. national magazine but most people still seem to think the degree of compression changes from focal length to focal length. Belief is so fervent that this is the first time I have mentioned it in over ten years.

[DanK]

The term "equivalent" to the best of my knowledge refers to the angle of view alone, not ancillary things like DOF, etc....

Richard,

you beat me to it. That is the only sense in which the two would necessarily be equivalent. that equivalence is simply a matter of trigonometry. They would not be equal in DOF (see http://photo.net/learn/optics/dofdigital/). And as Colin points out, if your concern is pixel count on the subject, you have to consider pixel density as well.

If you want a nice shallow DoF for say portrait work - go FX

That is only true if you are opening your lenses as wide as they go. If not, you can just change the aperture of the crop to compensate for the smaller aperture. There is a calculator on one of the tutorial pages on this site that shows by how much, but it is not a great deal.

Dan

[lukaswerth]

The issue is about f-stops. The f-stop determines for any given focal length the area of sharp focus. Period. The angle of view is determined, however, by the relation of the focal length to the image capturing device (sensor or film). So, for a 8x10" camera (where 8x10" is the film format) a normal lens, the equivalent to 50mm on full sensor, is 300 or 360mm (depending on the manner of calculation), for a 4x5" camera it is 150mm or 180mm, for a Mamiya 6x7 it is about 110mm. With a 300mm lens you get the depth of field of a 300mm lens, no matter what. In the 8x10" format the largest f-stop for exposure is usually f22, going easily down to f64, you tilt (applying the Scheimpflug rule), and you do not enlarge that much for a given print size.
The same principle holds for full and cropped sensor sizes.

Lukas

[William W]

I've been meaning to do this for ages but never got the time or the connections to gel.

I think that doing these types of practical exercises is of extreme value.

WW

[adrichu]

Would that mean that if i use a 25mm on a m4/3 (x2) body, i would have the same view of a 50mm on a full frame, but would be unable to use that for portraits because of the distortions on the face (since 25mm is very wide)? I know that 50mm lenses are ideal for portrait photography, but using a 50mm on a m4/3 would give me the equivalent of a 100mm view, which would have to place me quite far from my subject. Does that make sense?

[Black Pearl]

In a word yes.

To be a little more specific the preferred lens for a head/shoulders portraiture would be 85-135mm so even a 50 is a bit wide.

[tclune]

Would that mean that if i use a 25mm on a m4/3 (x2) body, i would have the same view of a 50mm on a full frame, but would be unable to use that for portraits because of the distortions on the face (since 25mm is very wide)? I know that 50mm lenses are ideal for portrait photography, but using a 50mm on a m4/3 would give me the equivalent of a 100mm view, which would have to place me quite far from my subject. Does that make sense?

Well, I learned studio portraiture on a 4x5 camera. The feeling in those days was that 35mm cameras were absurdly inappropriate for studio work because of the kind of thing you mention. Draw your own conclusions.

[lukaswerth]

Would that mean that if i use a 25mm on a m4/3 (x2) body, i would have the same view of a 50mm on a full frame, but would be unable to use that for portraits because of the distortions on the face (since 25mm is very wide)? I know that 50mm lenses are ideal for portrait photography, but using a 50mm on a m4/3 would give me the equivalent of a 100mm view, which would have to place me quite far from my subject. Does that make sense?

In a word, no. The crucial thing is: the concept of focal length is only meaningful in relation to the image capturing device.
The conventional formula is: normal lenses are considered those whose focal length is about the same as the diagonal length of the image capturing device (sensor/film). 50mm is actually a bit long for 35mm film cameras / full-frame sensors (should be more like 42mm), but this convention has crept in since the first Leica was built. If the linear dimension of this 35mm size is halved (from 24x36mm to 12x18mm) which reduces the area of the sensor/film to 1/4th, your equivalent to 50mm becomes 25mm, and there will be not any more or less distortion, because this will be your normal lens (no wide-angle any more). What changes is the area of sharp focus: you will get roughly the same area sharp with f4 as with f8 with 50mm on 35mm/full-frame.

--Oh yes, one thing more: the common ideal focal length on 35mm/full-frame is 85mm, not 50 - but that is certainly open to taste/distance of the subject. 100mm is also a very good focal length for this (on full-frame!)

Lukas

[Inkanyezi]

There are a few things mixed up in this discussion.

The "equivalent focal length" refers to angle of view as mentioned before, but no other entity.

To understand the DOF issue, for some, it is useful to think of the sensor size as determinant, while others prefer to think of it as a focal length issue. Both are of course relevant to a large degree, but it actually boils down to the size of the entrance pupil of the lens and the distance to the subject. For a very small creature, as an ant, most distances that are "small" to us, as the length of a foot for example, are large. Same for a small camera, all distances become relatively larger, compared to its sensor size and focal length. Distance is a determinant for DOF. Hence, a small format camera with a short "normal" focal length will have larger DOF, as the distances are relatively larger.

Looked at it from the other side, from the subject, it is easier to fathom, because from there, you see the entrance pupil of the lens. With a compact camera, you might use a focal length of about 7 mm when taking a portrait, and its largest aperture might be around f/5.6 at that focal length, an aperture just a tad larger than a millimetre, which will look no larger than a print period viewed from 5' distance. Its spatial angle when viewed from this distance is very small, and it is this spatial angle that determines DOF and background blur. The background will not be blurred with the compact camera, even though it might have the same angle of view as a larger camera with let's say an 85 mm lens.

This larger camera with the 85 mm, when using f/5.6 will have an entrance pupil that is abour 1.5 cm, considerably larger than the puny compact camera. Viewed from a distance of 5' it will certainly not look just like a point, but as a rather large hole. The spatial angle is much larger, so the background will be blurred, and DOF is much shorter.

So it is the size of the entrance pupil, when viewed from front, and the distance between the camera and the subject that determines DOF. The spatial angle of the entrance pupil viewed from the subject is the determinant, no matter which sensor or film size we use. For small sensors, a shorter focal length will always be used for the same field of view, and thus the aperture will be smaller and the spatial angle of it viewed from the subject is also smaller. Therefore the smaller sensor camera has larger DOF than the larger one, when the angle of view is the same and when using the same relative aperture. To get equal DOF a larger entrance pupil is needed, hence a larger relative aperture. For a 4/3 sensor compared to FF, the difference is 2 full F-stops. The µ4/3 camera will need a 50 mm f/1.4 to get the same DOF and background blur as a FF camera with a 100 mm f/2.8 lens. For the difference between FF and crop sensor (FX/DX), roughly one full stop is the equivalent value, so a 70 mm f/2 would render the same DOF on a crop camera as a 100 mm f/2.8 on FF or 50 mm f/1.4 on 4/3.

When using the Metabones® Speed Booster a 100 mm f/2.8 becomes a 70 mm f/2, and thus both properties, angle of view and DOF remain the same, while the relative aperture will be one stop faster. Accordingly, a Speed Booster changes a 70 mm f/2 lens into a 50 mm f/1.4, retaining DOF and angle of view for a µ4/3 camera as the lens without booster on a crop camera, while "speed" (relative aperture) doubles.

[Black Pearl]

Love the idea of the Speed Boosters - if/when I get a XT-1 system this year I might just invest.
Currently reading the White Paper on them.

[ajohnw]

I've been meaning to do this for ages but never got the time or the connections to gel.

People often talk about lens focal lengths giving the equivalent between cropped bodies and full frame bodies but there will always be the underlying fact that a particular lens will always be a particular lens and its characteristics will always be the same.

A 50mm is a 50mm no matter what. It might give the equivalent focal length of a 75mm on a (1,5x) crop camera but it will always be a 50mm. I know there are often (heated) arguments around this so I thought I'd have a bit of fun. As there are few 75mm lenses knocking about I went with a 35mm lens on a Nikon DX (1.5x crop) camera and a 50mm on a FX (FF) body.

Both shot from the same position, both shot with exactly the same settings:
Full manual mode: 1/40 sec; f/2.8; ISO 400
Both NEF files opened in Camera RAW 7.0 with all the settings synchronised. I aligned the layers and cropped the edges very slightly as the 35mm is the equivalent to 52.5mm not 50mm when multiplied by 1.5 to make the shots as close as possible.

Nikon D300s (12mp on a DX sensor) + 35mm:


Nikon D3 (12mp on a FX sensor) + 50mm:


As you can see the foreground/background separation between the two is significantly different even thought the equivalent field of views are the same. Another thing to note is the massive pixels on the D3 give a far nicer shadow rendering than the smaller ones on the D300s and though you can't see it there was far less noise visible when viewed at 100%.

As I said a bit of fun I've been meaning to do for ages.

If you want a nice shallow DoF for say portrait work - go FX
If you want loads of it for say landscape/macro - DX still has its place.

I can't help feeling that the foreground background appearance difference is mainly down to different depths of field. In other words the FX lens would have to be stopped down to achieve the same DOF as the DX or the other way round. There are some feature size changes. Some of that might be down to the crop factor not being exactly 1.5. The dx sensor is 35mm / 1.528 height and / 1.525 width. As the weather is wetter than ever I had a go a producing a difference image. One image 100% opacity and the other 50 and layer mode set to difference. This has to be a hard test to do. Still life might be easier.



Speed boosters have been available for telescopes for a long long time but called focal length reducers - aperture remains the same, focal length less so the F ratio is faster. Nothing magic about them as the image circle size is reduced increasing the concentration of light making it brighter. I reckon that they must reduce depth of field too. I'd guess if these don't reduce the image size on the sensor they must make use of light that doesn't currently hit it. Personally I would wait till rather a lot had been sold before buying one - vignetting for instance could be a problem if the whole image is needed. I suspect this patent will pend for ever. They are ever so expensive, see link to get a good idea of real cost.

http://agenaastro.com/antares-1-25-0...l-reducer.html

To be fair some are dearer.

John
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