The Perfect Coin Lens

I've been thinking recently about the requirements for imaging coins of different sizes, imaging variety details, etc and if there might be one lens that can do it all well. At first blush most would conclude "no way" but let's review the requirements before going there:

Maximum aperture: most of the cameras we use have a DLA (Diffraction Limited Aperture) of around f7. Some newer high MP cameras have DLA of around f6, while older models are around f10. Apertures smaller than the DLA (larger f-number) begin to show blurring due to diffraction, but it's not really visible until at least one stop beyond the DLA, and even at 2 stops beyond might not be too objectionable. Thus a good "target" aperture is in the f8-f11 range, leaning toward the upper end if depth of field is needed, or at the lower end if maximum sharpness is desired. This is working (effective) aperture, so depends on the magnification by feff = finf * (M + 1)

Imaging larger coins: magnification is lower for larger coins, so the effective aperture is larger, allowing you to stop the lens down to get more depth of field while still maintaining good sharpness. Shooting Dollars on APS-C requires M ~ 0.35, so a nominal aperture of f8 keeps the effective aperture below f11, and gives both good sharpness and depth of field. If a newer camera with smaller DLA, or a Full Frame camera is used, then f5.6 may be a better choice. Full Frame requires M ~ 0.6, higher than APS-C because the sensor is larger. Nominal aperture of f5.6 gives an effective aperture of f9 for Full Frame, still within the f8-f11 range. In any case, most all lenses that would be considered for coin photography have optimum apertures of f5.6 or larger, so finding a lens for Dollars is not an issue.

Smaller Coins: the situation for smaller coins is very different than for larger ones. The magnification required for Dimes on APS-C is ~0.8, and on Full Frame is ~1.3. To keep within the f8-f11 range, this requires the lens to have maximum aperture of f5.6 for APS-C, and f4.7 for Full Frame. Most lenses have best performance a stop or two down from their maximum aperture, so this means a lens to shoot small coins like Dimes should have maximum aperture of f2.8-f3.5. Some lenses which are good wide open, like the 75ARD1, can be used with full performance and indeed this is the "sweet spot" for such duplication lenses, which are optimized for performance around M=1. Note however, that "dedicated" macro lenses generally don't go beyond M=1, so shooting Dimes on Full Frame is not even possible without adding extensions to get to M=1.3, and smaller coins like Gold Dollars, Trimes, etc need even more extension. A teleconverter can be added to increase the magnification, but this also decreases maximum aperture. Most dedicated macro lenses don't respond well to going beyond 1:1, and require stopping down further to achieve good performance. This is a good reason for coin photographers to stick with APS-C rather than Full Frame cameras in order to reduce the magnification requirements and enable imaging of the full range of coins within the limitations of readily-available optics. It also is a good reason why duplication lenses optimized around M=1 are an excellent choice for smaller coins.

Variety marker imaging: This is where the difficulties really begin, since the feff = finf * (M + 1) formula starts to rapidly narrow the available options. Many variety markers (die cracks, scratches, breaks, etc) can be imaged effectively at M=2. Dedicated macro lenses need long extensions to achieve M=2, and their performance suffers since this is well beyond their specifications. A 2x teleconverter can be used, bringing a typical f2.8 macro lens at its optimum aperture of f4 at M=1 to f16 at M=2, well into diffraction territory. A better choice is a duplication lens, which generally still perform well at M=2. The 75ARD1 at nominal f4 achieves effective f12 at M=2, just outside the range we set for best performance. The best lens available for M=2 is the Canon 35mm f2.8 Macrophoto lens (35MP), which has optimum aperture of f3.3-f4 at M=2, so achieves effective aperture of f10-f12 and produces very sharp images. Unfortunately, the 35MP is limited to a minimum magnification of around M=1, so is not useful for imaging of larger coins.

Variety detail imaging: Let's use the Lincoln Cent "money shot" as the example here. On APS-C, a magnification of M=5 frames the full date and MM of a Lincoln Cent with just a little room around them. This is an excellent magnification to show RPMs and the position of the MM vs the date, or Doubled Dies on the date. To keep within the f11 range at M=5 requires a nominal aperture of f1.8. Very few lenses (none, I believe) are capable of this feat. A lens such as the Canon MPE-65 is capable of a maximum of M=5, but it needs to be stopped-down to f4 or f5.6 for its best performance, putting it at f24-f33 effective, deep into diffraction territory. Plus, its minimum magnification of M=1 limits its use for full-coin imaging similar to the 35MP.

The best lenses for variety detail imaging are microscope objectives. The Mitutoyo MPlan APO 5x has a nominal aperture of f3, so that at 5x it is at f18. This is well into diffraction-limited territory, but is nearly as good as you can get at this magnification. The 4x Nikon Plan Apo has a nominal aperture of f2, and can easily be pushed to 5x, resulting in f12 effective aperture. These are the best performers you can get at these magnifications. A more modest Nikon M5 has nominal aperture of f4.2, resulting in effective aperture of f25 at 5x. The good performance of this lens has been well-documented in this forum, yet it can easily be bettered by the more capable Mitutoyo or high-end Nikons. Yet none of these microscope objectives can begin to image full coins, so they cannot stand on their own as a full-range coin imaging lens.

The above descriptions of the requirements across the full magnification range used for coin photography indicate that it is a difficult task to utilize one lens across that range with a high level of performance. But is it impossible? What sort of lens might work for this task? The lens would need to have a wide maximum aperture; have strong performance wide open; and be optimized not just in one magnification range, but in two ranges, which would allow a much wider total optimum range. A couple lenses like this do exist:

75mm f4.5 Rodenstock Apo Rodagon D M1:2
95mm f2.8 Nikon Printing-Nikkor M1:2


Why are these so special, and what does it mean to be "optimized in two ranges"? The key here is that these lenses are optimized around M=0.5 when forward mounted, and M=2 when reverse mounted. Their usable range forward mounted is M=0.25 to M=1, and reverse mounted from M=1 to M=4 (with diminishing performance above M=2). It is this two range characteristic that makes them so special.

Since both these lenses are outside their optimum range at M=5, a better result can be achieved by using them at M=2.5 along with a 2x teleconverter to achieve M=5. As long as the teleconverter is of high quality, there is very little drawback to doing this, and it keeps the lenses themselves operating at nearly their design optimum.

The Printing-Nikkor will obviously outperform the 75ARD2, with its wider maximum aperture and true apochromatic correction, but at a far higher price. 95PN's sell for $1200-$1800 typically, while 75ARD2's can be had for <$300. How much better is the 95PN vs the 75ARD2 over the whole range? As you might expect, for full-coin imaging over the whole range of coin sizes, stopped-down to the apertures discussed above, you will likely not see much difference between the lenses. Both are well-corrected for chromatic aberrations, and as most folks on this forum have learned over the last few years, lighting and other technique swamp the small differences that are present between high quality lenses.

Where the differences will become apparent is in pushing the lenses to M=5 for variety imaging. The 75ARD2 has max aperture of f4.5, so at M=5 the effective aperture will be f27, far into diffraction territory. The 95PN has max aperture of f2.8, so at M=5 the effective aperture will be f17, about the same as the Mitutoyo MPlan APO 5x objective. Based on this, the 95PN should produce much sharper images at M=5, and indeed it does. See the images below to compare:

The Lincoln Cent "money shot" using the 75ARD2 with 2x teleconverter:


A 100% crop from the 75ARD2 image above:


The same shot using the 95PN:


A 100% crop from the 95PN image above


For the images above, all sharpening was turned off and no postprocessing other than cropping was done. The 75ARD2 image required 4 shots in the stack, while the 95PN required 8. This in itself is a strong indication of quality. That said, the 75ARD2 image is not bad at all, though it's not quite as good as you can get from an M5 objective. The 95PN image is really good, better than an M5, but not quite as good as you would get from the Mitutoyo 5x objective.

Bottom line, the 95PN can be used effectively for top quality images across the whole range of coin sizes, variety markers, and even for variety details shots at 5x magnification. One lens can do it all, and because of this I would call the 95PN "the perfect coin lens".