Nikon Macro Lens, effective aperture

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Bill Janes Senior Member • Posts: 1,907
Nikon Macro Lens, effective aperture
1

As you focus closer towards 1:1 magnification with a classic Nikon macro lens (Micro Nikkor in Nikon speak) the lens is extended and the effective aperture decreases. With more recent Nikon macro lenses the front element of the lens does not move and the overall length of the lens does not change. Close focusing is obtained by internal movement of lens elements, resulting in a decrease of focal length.

The classic formula of determining the effective focal length is fe = fm * (m+1), where m is the magnification, fm is the marked or nominal aperture and fe is the effective aperture. Chipped Nikon lenses report the effective aperture. With an f/2.8 macro focused at 1:1, the effective aperture is reported as f/5.6.

A more accurate formula for the effective aperture is fe = fm * (m/p +1), where p is the pupil magnification ratio (see here for details). For normal focal length macros (55 or 60 mm) the pupil ratio is often near 1:1 and the simpler formula gives reasonably accurate results. However, with telephoto macros, p is often considerably less than 1:1).

Bill Claff's Optical Bench gives p for many lenses. For the Nikon 105 mm f/2.8 OS micro Nikkor it is 0.74, 0.65, and 0.58 at infinity focus (zero magnification), 0.5 m, and 1:1 m respectively. I'm not sure which of the several 105 f/2.8 Micro Nikkors this is, but presumably one that extends the front element on close focusing (such as the AF Micro Nikkor 105 mm 1:2.8D which is screw driver focus with extension of the front element on close focusing.

With the latest AFS Micro Nikkor 105 mm f/2.8 G (an internal focusing lens) p is 1.06, 0.56 and 0.3 at infinity, 0.5 m, and 1:1m respectively. P changes more with close focusing with this lens, and in this case, internal focusing increases the variability of p.

With both of these lenses focused at 1:1, the effective aperture is reported as f/5.6 in accordance with the simplified effective aperture formula. Accounting for p, the effective aperture for the former lens at 1:1 with the aperture set at f/2.8, is f/7.6. With the latter AFS lens, the effective aperture with the lens set at f/2.8 is f/12.1. With this lens set at f/8, the effective aperture is f/34.7, well in diffraction territory.

I don't know how the chipped lenses account for p, but the above considerations indicate that it is ignored. These differences are significant with everyday photography, and additional discussion is invited.

Bill Janes

Leonard Shepherd
Leonard Shepherd Forum Pro • Posts: 19,572
Re: Nikon Macro Lens, effective aperture

Bill Janes wrote:

With the latest AFS Micro Nikkor 105 mm f/2.8 G (an internal focusing lens) p is 1.06, 0.56 and 0.3 at infinity, 0.5 m, and 1:1m respectively. P changes more with close focusing with this lens, and in this case, internal focusing increases the variability of p.

With both of these lenses focused at 1:1, the effective aperture is reported as f/5.6 in accordance with the simplified effective aperture formula. Accounting for p, the effective aperture for the former lens at 1:1 with the aperture set at f/2.8, is f/7.6. With the latter AFS lens, the effective aperture with the lens set at f/2.8 is f/12.1. With this lens set at f/8, the effective aperture is f/34.7, well in diffraction territory.

I don't know how the chipped lenses account for p, but the above considerations indicate that it is ignored. These differences are significant with everyday photography, and additional discussion is invited.

This is complex territory

"P" is usually only an issue when focussing closer than 1/10 life size

I am not sure if you have the 105 VR macro - but if not try to handle one on a DSLR.

Put the lens on a camera, aperture priority at aperture f4, look into the front of the lens, press and hold the depth of field preview and watch the physical size of the aperture change from well stopped down at infinity to about wide open at in 1:1 focus.

Then repeat looking at the top plate read out and note the exposure time between infinity and 1:1 stays the same - even though if the lens was a symmetrical design (which it is not) the exposure time should increase approaching 1:1 magnification.

Next set the lens at infinity f2.8 (aperture wide open), change focus to 1:1 and (as the lens cannot open wider than wide open) watch the exposure time increasing.

What the Nikon system seems to do with the the 105 VR macro lenses is at f4 at 1:1 focus is to open up the aperture to get an f2.8 exposure when showing f4 on the exposure read out.

Nikon "gets" the exposure right at 1:1 by opening up the aperture by 1 stop, with the other 1 stop being from focus breathing - to get the 2 stop 1:1 exposure increase needed with a symmetrical lens.

Back to the top plate read-out - you can set f51 at 1:1 focus and observe it changes to f32 by changing focus to infinity.

Summing up - at 1:1 you get a correct exposure with 1 stop less depth of field than for the 1:1 aperture read out indicates - and a 1 stop brighter aperture than with a symmetrical lens.

Why do the 60mm AF-S, the 105 G and the 200 D macro work in this unusual way?

I have not been able to find out from Nikon.

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Leonard Shepherd
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bclaff Forum Pro • Posts: 10,069
Re: Nikon Macro Lens, effective aperture
1

FWIW, the 105mm correctly reports f/4.8 not f/5.6 at 1x,

For some details see:

Focal Length at Closest Focus - 105mm f2.8G IF-ED AF-S VR Micro-Nikkor

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JHern
JHern Forum Member • Posts: 92
Re: Nikon Macro Lens, effective aperture

Deriving the simple formulas is easy when we can assume that the light rays are parallel to the lens axis...while this is only strictly true for objects at infinity, it is a very good approximation until one gets close. As the objects get closer, the light rays are not parallel to the lens axis, but rather are spreading outward (diverging) on their way from the subject to the entrance pupil, and this is the geometric context that can be used to derive the correction factor for aperture. I've never done the full derivation, but I should sit down and work it out for my own curiosity. Will follow this thread...

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bclaff Forum Pro • Posts: 10,069
Re: Nikon Macro Lens, effective aperture
1

JHern wrote:

Deriving the simple formulas is easy when we can assume that the light rays are parallel to the lens axis...while this is only strictly true for objects at infinity, it is a very good approximation until one gets close. As the objects get closer, the light rays are not parallel to the lens axis, but rather are spreading outward (diverging) on their way from the subject to the entrance pupil, and this is the geometric context that can be used to derive the correction factor for aperture. I've never done the full derivation, but I should sit down and work it out for my own curiosity. Will follow this thread...

Keep in mind that effective aperture is all about the exit pupil, not the entrance pupil.

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Bill ( Your trusted source for independent sensor data at PhotonsToPhotos )

JHern
JHern Forum Member • Posts: 92
Re: Nikon Macro Lens, effective aperture

bclaff wrote:

JHern wrote:

Deriving the simple formulas is easy when we can assume that the light rays are parallel to the lens axis...while this is only strictly true for objects at infinity, it is a very good approximation until one gets close. As the objects get closer, the light rays are not parallel to the lens axis, but rather are spreading outward (diverging) on their way from the subject to the entrance pupil, and this is the geometric context that can be used to derive the correction factor for aperture. I've never done the full derivation, but I should sit down and work it out for my own curiosity. Will follow this thread...

Keep in mind that effective aperture is all about the exit pupil, not the entrance pupil.

My thinking is more based on light transmission/flux.

Here is a simple derivation of scaling relationships that we all know well....consider 2 lenses: a 100mm and 50mm focal length, and pointed at a very distant object that is emanating light rays parallel to the lens axis under steady conditions. The 100mm lens covers 1/4 the perpendicular area of the object as the 50mm lens*. This 1/4 coverage of 2X focal length means the longer one receives 4X less light from the object in the same exposure time (T). To have the same total light flux (exposure), the lens with twice the focal length (L) needs to have 4X the pupil area (or 2X the pupil diameter, D) compared to the shorter focal length lens. Total light flux delivered onto the sensor (exposure, E) therefore goes like E/Eo=(T/To)*D*D/(L*L) where Eo is a reference exposure value at a reference exposure time To. Since E/Eo=(T/To)/(F*F) is how the f-number (F=1.4, 2.0, 2.8, 4.0, 5.6, etc.) is defined, it follows that F=L/D...but only under the assumed conditions.

This breaks down when the light rays are no longer parallel to the lens axis, when the object in question is very close to the lens. A correction factor is needed for the geometric spread of light rays emanating from the subject to the lens. If you account for this correction factor, then you'll find that the F is higher than the value for the object at infinity.

...

*That is, you could take four 100mm photos left-right-up-left shifting by increments of frame edge, put the photos together edge-to-edge, and you get the same frame of view/object coverage as the 50mm can grab in one shot.

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bclaff Forum Pro • Posts: 10,069
Re: Nikon Macro Lens, effective aperture
1

JHern wrote:

bclaff wrote:

JHern wrote:

Deriving the simple formulas is easy when we can assume that the light rays are parallel to the lens axis...while this is only strictly true for objects at infinity, it is a very good approximation until one gets close. As the objects get closer, the light rays are not parallel to the lens axis, but rather are spreading outward (diverging) on their way from the subject to the entrance pupil, and this is the geometric context that can be used to derive the correction factor for aperture. I've never done the full derivation, but I should sit down and work it out for my own curiosity. Will follow this thread...

Keep in mind that effective aperture is all about the exit pupil, not the entrance pupil.

My thinking is more based on light transmission/flux.

Here is a simple derivation of scaling relationships that we all know well....consider 2 lenses: a 100mm and 50mm focal length, and pointed at a very distant object that is emanating light rays parallel to the lens axis under steady conditions. The 100mm lens covers 1/4 the perpendicular area of the object as the 50mm lens*. This 1/4 coverage of 2X focal length means the longer one receives 4X less light from the object in the same exposure time (T). To have the same total light flux (exposure), the lens with twice the focal length (L) needs to have 4X the pupil area (or 2X the pupil diameter, D) compared to the shorter focal length lens. Total light flux delivered onto the sensor (exposure, E) therefore goes like E/Eo=(T/To)*D*D/(L*L) where Eo is a reference exposure value at a reference exposure time To. Since E/Eo=(T/To)/(F*F) is how the f-number (F=1.4, 2.0, 2.8, 4.0, 5.6, etc.) is defined, it follows that F=L/D...but only under the assumed conditions.

This breaks down when the light rays are no longer parallel to the lens axis, when the object in question is very close to the lens. A correction factor is needed for the geometric spread of light rays emanating from the subject to the lens. If you account for this correction factor, then you'll find that the F is higher than the value for the object at infinity.

...

*That is, you could take four 100mm photos left-right-up-left shifting by increments of frame edge, put the photos together edge-to-edge, and you get the same frame of view/object coverage as the 50mm can grab in one shot.

Your comment has nothing to do with effective aperture (also see Numeric Aperture (NA)) which always has to do with the exit pupil. Effective aperture has to do with how light is projected not how it is collected.

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Leonard Shepherd
Leonard Shepherd Forum Pro • Posts: 19,572
Re: Nikon Macro Lens, effective aperture

JHern wrote:

My thinking is more based on light transmission/flux.

Here is a simple derivation of scaling relationships that we all know well....consider 2 lenses: a 100mm and 50mm focal length, and pointed at a very distant object that is emanating light rays parallel to the lens axis under steady conditions. The 100mm lens covers 1/4 the perpendicular area of the object as the 50mm lens*. This 1/4 coverage of 2X focal length means the longer one receives 4X less light from the object in the same exposure time (T). To have the same total light flux (exposure), the lens with twice the focal length (L) needs to have 4X the pupil area (or 2X the pupil diameter, D) compared to the shorter focal length lens.

Most knowledge (rather than thinking) comes to a different conclusion.

The sun which illuminates the earth is so far away that light illuminating a subject reaches it in parallel lines and is reflected off any surface parallel to the sensor in parallel lines.

The difference in light intensity reflecting off an object at 10 yards or 20 yards is nil.

All the 100mm does is accept the same intensity of light as the 50mm - and exposure is primarily based on light intensity.

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Leonard Shepherd
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bclaff Forum Pro • Posts: 10,069
Re: Nikon Macro Lens, effective aperture

Leonard Shepherd wrote:

JHern wrote:

My thinking is more based on light transmission/flux.

Here is a simple derivation of scaling relationships that we all know well....consider 2 lenses: a 100mm and 50mm focal length, and pointed at a very distant object that is emanating light rays parallel to the lens axis under steady conditions. The 100mm lens covers 1/4 the perpendicular area of the object as the 50mm lens*. This 1/4 coverage of 2X focal length means the longer one receives 4X less light from the object in the same exposure time (T). To have the same total light flux (exposure), the lens with twice the focal length (L) needs to have 4X the pupil area (or 2X the pupil diameter, D) compared to the shorter focal length lens.

Most knowledge (rather than thinking) comes to a different conclusion.

The sun which illuminates the earth is so far away that light illuminating a subject reaches it in parallel lines and is reflected off any surface parallel to the sensor in parallel lines.

The difference in light intensity reflecting off an object at 10 yards or 20 yards is nil.

All the 100mm does is accept the same intensity of light as the 50mm - and exposure is primarily based on light intensity.

The reasoning given is more light "light grasp" eg. entrance pupil area times solid angle.
That's sort of "OK" but it isn't effective aperture.

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Leonard Shepherd
Leonard Shepherd Forum Pro • Posts: 19,572
Re: Nikon Macro Lens, effective aperture

bclaff wrote:

The reasoning given is more light "light grasp" eg. entrance pupil area times solid angle.
That's sort of "OK" but it isn't effective aperture.

"Sort of "OK"" helps with a lens that physically opens the size of the aperture used changing focus distance between infinity and minimum focus - as the 60 GG, 105G and 200 D generally do.

These 3 macro lenses cannot open up the size of the aperture when starting at infinity - and then change the focus time instead.

The reason for these macro lenses maintaining an infinity focus distance exposure time by a combination of "lens breathing" and changing the physical size of the aperture has to the best of my knowledge never been given by Nikon.

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Leonard Shepherd
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bclaff Forum Pro • Posts: 10,069
Re: Nikon Macro Lens, effective aperture

Leonard Shepherd wrote:

bclaff wrote:

The reasoning given is more light "light grasp" eg. entrance pupil area times solid angle.
That's sort of "OK" but it isn't effective aperture.

"Sort of "OK"" helps with a lens that physically opens the size of the aperture used changing focus distance between infinity and minimum focus - as the 60 GG, 105G and 200 D generally do.

These 3 macro lenses cannot open up the size of the aperture when starting at infinity - and then change the focus time instead.

Did this sentence get mangled?

The reason for these macro lenses maintaining an infinity focus distance exposure time by a combination of "lens breathing" and changing the physical size of the aperture has to the best of my knowledge never been given by Nikon.

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Leonard Shepherd
Leonard Shepherd Forum Pro • Posts: 19,572
Re: Nikon Macro Lens, effective aperture

bclaff wrote:

These 3 macro lenses cannot open up the size of the aperture when starting at infinity - and then change the focus time instead.

Did this sentence get mangled?

Yes. I should have said starting at infinity with the lens wide open.

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Leonard Shepherd
In lots of ways good photography is much more about how equipment is used rather than anything else.

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