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Archive 2015 · Who Cares about the Inverse - Squire Law?

  
 
Bob Culver
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p.1 #1 · p.1 #1 · Who Cares about the Inverse - Squire Law?


Who does this law effect and why should you care?

In the exercise below, I describe the difference between the Nikon 105mm f2.8 D Macro lens with internal focusing verses a primary lenses mounted onto extension rings. The focus of this experiment is the light catching ability of both lenses while using the same F-stop for the test exposures in macro mode.

I am an amateur photographer, and graduate of Brooks Institute class of 1979. I have been using my Nikon F Photomic until early 2005. Up to that point for Macro photography, I used my bellows and a dedicated bellows 100mm lens, (A. Schacht Ulm – Travegar 1:3.3/100 R).

With the purchase of my Nikon D70s, I purchased AI extension rings and a Series E 100mm f2.8 lens. I found this combination very satisfying, acquiring good captures. The resolution was excellent and images with good contrast. I use a combination of flash and natural lighting, whatever works for the particular image.

My point is that I read somewhere, but was unable to confirm where of what I read until now, that an internal focusing lens, (as Nikon’s CRC close-range correction system in the Macro lens) will deliver more light to the film plane. My present AI extension rings and 100mm f2.8 lens configuration was problematic where I needed more light do to the inverse square law, while the lens was fully extended requiring the use of a flash for even slow moving subjects. While researching for newer macro lenses to see if they incorporated the internal focusing, I came upon the 105mm f2.8 D macro lens. So I purchased one and to my surprise, the internal focusing had an advantage regarding exposure. See the test chart below. I found the image transmitted to the film plane (sensor) was more than 2.5 times brighter than manual focusing lenses mounted onto extension rings at the same magnification of nearly 1:1.

I took a series of exposures (at one full stop intervals) using the Series E 100mm lens mounted onto a series of extension rings equaling 54mm extension. A magnification of about 1:0.85 with the lens focusing ring also extended. Then I took a series of exposures (at one full stop intervals) with the 105mm f2.8 D Macro lens set for the same magnification. I plotted the results below. With the 105mm, I was unable to go below F4 because that is the limit with the lens near fully extended. As you can see, the 105mm can deliver more light than using the Series E 100mm lens on extension rings. In addition, all the exposures fell exactly in proper exposure range, using the D70s Hysteresis display screen, and all image exposures resulted in equal intensity values. With this new lens, I expect to capture more close-ups hand-held and or on a tripod shooting objects that have a tendency to move. In addition, I have noticed the two lenses seem to have similar quality aspects regarding sharpness and contrast. This remains to be seen with my continued use of this new lens.

Also, one note; I keep reading on other peoples reviews that they are concerned about the light fall-off while extending for macro thinking their new lens was defective. Obviously, they were not using a Nikon CRC lens but using a lens whose rear lens element moves with the entire lens barrel. This is a law of physics, the inverse square law. On their lens, the rear lens element can extended twice the distance from the film plain will receive a quarter (1/4) of the illumination – or two stops less light. This principal is true for light of any type except for possibly lasers. Moving the rear lens element away from the film plane (sensor) will involve light fall off, and follows the inverse square law. I also included a chart with plots showing magnification influence on exposure between the two lens test subjects. Note at f8 that the two plots should converge when both lens are set to focus at infinity. Also note the 105mm f2.8 D has the same exposure index, (shutter speed) at f8 no matter what magnification is used.

As I noted before, the image quality of the 105mm “D” macro lens seems comparable to the 100mm Series “E” lens for the most part. I found the 105mm “D” macro lens can be stopped down farther without the same chromatic abrasion issues as the Series “E” lens. Also, the contrast is generally a bit better in the 105mm Macro “D” lens.


THE TESTS;
The 100mm Series E is mounted onto extension tubes equil to 54mm extension. All exposures for both lenses were at 1:0.82 magnification, I set the F-stop and adjusted for proper exposure via the shutter speed.

See Exposure Comparison chart.

The Orange lines on the graph are referenced to the shutter speed of 1/3 second and the Green lines are referenced to the aperture of f5.6. In either case the exposure increase using the 105mm D lens was greater than 2.5 stops.
The table below has the actual data used for the plot “Exposure comparison”.

For this plot, I preset the aperture of both lenses to f8, set magnification at four values of both lenses and compensated for exposure with the shutter speed, but only needed to adjust Shutter Speed on the 100mm Series E lens.


Table below is the Mag. Vs. Exposure data.
lens
100mm 105mm
ss mag ss mag ss
1/6 1:0.62 0.1667 1:0.62 0.0400
1/10 1:0.39 0.1000 1:0.39 0.0400
1/13 1:0.24 0.0769 1:0.24 0.0400
1/16 1:0.10 0.0622 1:0.10 0.0400


Conclusion;
Upon examining the captures from both lenses, I found that the 100mm Series E lens to be an excellent quality macro lens when paired with extension tubes or even a bellows. Contrast is only slightly improved using the 105mm D Macro. Chromatic abrasion exists in the 100mm Series E with some color fringing evident at extreme magnification of the images. This color fringing was almost undetectable in the Series E lens. No evidence of color fringing at all on the 105mm D Macro and the 100mm Series E was very slightly softer looking at extreme magnification of the images.

The 100mm Series E macro combination is somewhat cumbersome where changing the extension rings or using the bellows, even worse. This is why I considered the 105mm D Macro in the first place. The 105mm D lens allows me to adjust magnification on the spot and the metering works like I would expect. I use the rear shutter flash function all the time and the 105mm D70s makes this easy.

The CRC is a great advantage for exposure concerns. An added bonus for this Nikon lens allowing faster shutter speeds and or stopping down for increased depth of field. One note; using the flash alone in my opinion detracts from the quality of the image aesthetically.







dedicated bellows 100mm lens, (A. Schacht Ulm – Travegar 1:3.3/100 R)







Series E 100mm lens







extension rings equaling 54mm




Sep 20, 2015 at 07:29 PM
Bob Culver
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p.1 #2 · p.1 #2 · Who Cares about the Inverse - Squire Law?


Sorry I pressed the send button rather the add new photos. Here are the tables.





Exposure Comparison chart.







Shutter speed table







Magnification verses Exposure







Data supporting the Magnification verses Exposure graph




Sep 20, 2015 at 07:37 PM
e6filmuser
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p.1 #3 · p.1 #3 · Who Cares about the Inverse - Squire Law?


It's a bit early in the morning to study your text in detail but two points emerge:

1) In macro, as you get closer, the inverse square law not longer applies for flash illumination, as the flash is not a point source. If you are using daylight it will, leaving you with the magnification factor.

The inverse square law can be ignored for sunlight, as any change in subject distance is infinitely small compared with the distance from the sun.

2) Many macro lenses have internal extension, Also, their focal length may change slightly as you rack them out.

Essentially, at a given aperture, you are dealing with magnification factor. Magnification, however achieved, spreads the light out from a smaller area over the same area of sensor, losing intensity. That requires longer exposure or wider aperture.

Harold



Sep 21, 2015 at 01:06 AM
Bob Culver
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p.1 #4 · p.1 #4 · Who Cares about the Inverse - Squire Law?


Hello Harold,
Item 1. You are indeed correct when using flash. When using the flash, adjusting magnification which requires moving closer increases light intensity from the flash the same amount as the decrease in light falling onto the film. Much of the time I like to mix flash with natural lighting and this is where I had issues. Regarding the sun, the inverse square law applies to the rear lens element to film plain only. Yes magnification is what effects this rear lens element to film plain effect.

Item 2. Also correct where macro lens of the internal focusing design are concerned. I have a 55mm Micro-NIKKOR 2.8 AI, and its real element moves with the magnification setting. This is also true for any prime lens mounted onto extension rings or onto a bellows. Most certainly a newer macro would be preferred.

Thank you for your comments. I should have included the item 1. scenario in my initial posting.

Bob



Sep 22, 2015 at 09:58 PM





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