Laowa 85 mm f/5.6 2x macro

When planning my purchase of the first few lenses for the Nikon Z8, I had to decide whether I need a new macro lens for this camera, and if so, which one best fits my needs and expectations. Photomacrography is one of my main types of photography, and the choice of a new macro lens for the Z8 must take into account the numerous macro lenses I already own, that can be used on this camera.

For work in the lab and on short trips, I can already count on the Laowa 100 mm f/2.8 2x, Laowa 25 mm f/2.8 2.5x-5x, Printing Nikkor 105 mm f/2.8 N, CoastalOpt 60 mm f/4 Apo, and the Minolta 5400 and Nikon Coolscan 4000 re-purposed scanner lenses mounted on helicoids.

My Nikon Z 24-120 f/4 S provides AF and focus bracketing at up to 0.39x, well in the close-up range, and my Nikon Z 180-600 f/5.6-6.3 VR at 180 mm up to 0.25x with a focus distance of 1.3 m.

The Nikon Z 105 mm f/2.8 macro could be handy. AF is not so useful by itself in photomacrography, but is necessary for in-camera focus bracketing, which eliminates the need for a motorized rail and controller and is much faster than the latter, especially in the field. On the other hand, this 105 mm is quite large and relatively heavy. There is a real risk that I would decide not to take it along on a long trip because of its size. I decided to wait indefinitely before getting the Nikkor Z 105.

There is also a Nikon Z 50 mm f/2.8 macro that costs and weighs little more than half of the Nikon Z 105, and provides AF and focus bracketing. I agree with many other photographers that 50 mm is quite short for a full-frame macro lens, but on the other hand this Z 50 mm macro takes one-quarter the space of the 105 mm macro. I will wait indefinitely also before getting this lens, because its short focal length will be a problem in practical use.

Nikon macro lenses in F and Z mounts do not exceed a 1x maximum magnification. The only F-mount macro lenses capable of AF when adapted to Z cameras with Nikon FTZ and FTZ II adapters are those in the AF-S series. In practice, this means the Micro Nikkor 105 mm f/2.8 G and Micro Nikkor 60 mm f/2.8 G. Neither is particularly exciting. The 60 mm is optically better than the 105 mm, but like the Nikon Z 50 mm macro, a bit too short in focal length.

The Tamron 90 mm f/2.8 DI III macro in Z mount is cheaper than the Nikkor Z 105, appears to be no less good optically, and has AF for those times I may need it. I was unable to confirm whether this lens allows focus bracketing.

Laowa has a large range of manual-focus macro lenses, many of them capable of magnification from 0 to 2x. Some Laowa lenses have a CPU, and Laowa has introduced a few new AF lenses in Nikon Z mount.

My actual choice of a new macro lens for the Z8 is the very small and lightweight Laowa 85 mm f/5.6 2x. Why one more fully manual 2x macro lens? The 85 mm is so small that the space it takes in my backpack is not a credible excuse for leaving it at home. The low speed of the 85 mm is the price to pay for the small size, and f/5.6 is actually quite adequate for use on a mirrorless camera. Pixel peepers may correctly observe that it cannot be equally sharp, fully open, as the best f/2.8 lenses, but I am more concerned with actual performance versus size for use in the field, where I usually shoot at f/8 to f/11. The 85 mm does become an effective f/16 lens fully open at 2x, which is at the limit of usability even on full frame. However, I do have better lenses to use if I should need pixel-peeping sharpness, or extensive field work at 2x.

Should I need a long-distance macro, I would probably choose the AF Micro Nikkor 200 mm f/4 (0x-1x), or possibly the Laowa 180 mm f/4.5 1.5x Ultra Macro if I can be convinced of its optical quality. The Laowa 180 works only in manual focus in the close-up and macro range. The Micro Nikkor 200 works only in manual focus on Nikon FTZ and FTZ II adapters, so they are equal in this respect. The Micro Nikkor 200 is a well tried-and-tested lens but large and heavy, while the Laowa 180 reaches 1.5x but is a newcomer. This, however, will be a decision left for another day.

The Laowa 85 mm in practice

The Laowa 100 mm (above figure, right) is one of the physically largest macro lenses of this brand. Factory-equipped with a Nikon Z mount, or in Nikon F mount like in the picture and mounted on a Nikon FTZ II adapter, it is remarkably long (162 mm from front to mounting flange, including the front protector filter that comes with the lens). For this reason, I prefer to use it on the Z8 with a Nikon FTZ adapter (the original version equipped with a tripod mount, now discontinued) and an Arca-compatible rail for easy attachment to a tripod or stand.

Figure 1 shows an odd difference between the two Laowa lenses: they focus in opposite directions from infinity toward shorter distances. The 100 mm focuses in the same direction as my Nikkor AF, AF-S, AI and AI-S lenses. All recent Laowa macro lenses seem instead to focus in the same direction as the 85mm.

Laowa describes the 100 mm as an internal-focus lens, but the optical surface visible at the top of the lens in the above figure is actually a protective filter. The lens can be used also after unscrewing this filter. Its main usefulness is to prevent dust and crud from lodging in the lubricant-smeared interior of the barrel when the lens optics are retracted within the barrel by focusing at infinity. Strictly speaking, this does not qualify as internal focus in an optical sense.

After cutting its teeth with its original 60 mm f/2.8 2x lens (which was the first lens capable of 0-2x magnification, as far as I know, and also retracts deep within its barrel at infinity focus), Laowa started churning out numerous additional 2x macro lenses of better quality, different focal lengths, and in different DSLR mounts. The 100 mm was one of the first, and is still marketed at present because of its remarkably good optical quality and reasonable price. Most of the more recent models are true internal-focus lenses with a fixed optical group at the front end of the barrel. This design takes advantage of the front group for correcting aberrations at different magnifications. A few more traditional macro lenses of other brands use a fixed rear group for the same purpose, which is mechanically simpler than a true floating group moved by a cam.

Most of the recent models of Laowa macro lenses are designed from the ground up for mirrorless cameras. Their optical scheme takes advantage of the short registration distance, and they cannot be used on DSLRs. A few of the Laowa macro lenses differ substantially from traditional macro lenses, both in appearance and capabilities. For example, the Laowa 25 mm f/2.8 2.5x-5x is among the latest, and is probably the best among only four or five comparable lenses in other camera systems. This includes an externally similar 25 mm f/2.8 2.5x-5x model branded AstrHori, which is apparently designed for use only on mirrorless cameras (the Laowa 25 mm is available also in DSLR mounts).

The Laowa 85 mm f/5.6 (above figure, center) is one of the Laowa lenses designed for mirrorless cameras. It is unique among modern macro lenses for its f/5.6 speed, which at first sight appears a questionable choice for a macro lens. At 1x, the conventional wisdom is that effective aperture is two stops higher than nominal aperture, so this lens is an effective f/11 lens at 1x. At 2x, it is an effective f/16 lens. Unless one intends to publish images shot with this lens at a small final size (e.g. on a web page), the 85 mm must be used fully open between 1x and 2x. It can be stopped down a little in the close-up range, and perhaps up to 2-3 stops with distant subjects.

On the other hand, the low lens speed is critical in achieving a narrow lens barrel. The filter mount is 46 mm, same as the Nikon Z 50 mm f/2.8 macro and the Olympus Micro 4/3 60 mm f/2.8 1x macro (Figure 1, left). This lens and the Laowa 85 mm are remarkably similar in physical size, allowing for the different sizes of the lens mounts and the slightly different registration distances, but the Olympus 60 mm only reaches 1x.

The front of the lens surrounding the optical surface of the front element carries the silk-screened lens model identification, Laowa logo and serial number. All scales and tick marks on the barrel, focus ring and aperture ring are engraved.

The 85 mm weighs around 300 g, depending on the lens mount, and is probably the smallest in volume among current and past Laowa macro lenses.

The magnification scale is farthest from the aperture index on the lens barrel, and this makes it difficult to set a repeatable magnification. The magnification scale should instead be placed closest to the aperture index, because in photomacrography one usually works by setting the lens at the desired magnification first, rather than the focus distance, and subsequently focuses by moving either the subject, or the camera and lens as a whole, relative to each other to focus. A future update of this lens should place the magnification scale in close proximity to the distance index mark, because in photomacrography the recommended method is to first set the magnification on the focus ring, and subsequently to focus by moving the camera and lens as a whole (or by moving the subject). With infrequent exceptions, the focus ring is used for actual focusing only in the non-macro range.

In the mean time, one can observe that each marking on the magnification scale corresponds to one marking on the metric distance scale. This can be useful to set the magnification with better repeatability.

The Z8 is a larger-than-average mirrorless camera, and the Laowa 85 looks very small when mounted on this camera. Figure 2 shows the lens focused at its maximum magnification, with the internal focus subassembly closest to the fixed front group.

Look at the red dot on the lens mount of the 85 mm. If it looks slightly off-center to the right and the lens looks not completely inserted into the mount of the camera, that's because it isn't. The bayonet mount of my 85 mm is probably defective, and the lens does not fully rotate in the camera mount and does not lock onto the camera. I have not contacted Laowa about this, have not found yet what causes this problem, and don't know whether I can easily fix it.

I have quite a few Nikon Z lens mounts available as comparison, most of them manufactured by Nikon, others third-party but known to mount correctly on my Z8, so I will eventually find out what deviates from the mechanical specifications in this Laowa lens. I will update this page with information once I learn more. In the mean time, I can use the lens, but carefully. It is held onto the camera only by friction of the bayonet lugs against the springs in the camera mount, and without care could twist in the camera mount and fall off while handling the camera and lens.

The lens arrived to me still factory-sealed in its box and with no visible signs of damage on the lens or packaging, so the problem was not caused by damage in transit, and the lens specimen is not a customer return. Commonly used parts like a lens mount are possibly shared by multiple lens models, and are very likely manufactured entirely by CNC machines in the hundreds during a single production run. This defective mount may be a one-off, the result of a temporary malfunction so unusual that Laowa does not bother to individually test the lens bayonets at any stage of lens production, or an entire batch of Laowa lenses with defective Z mounts may have made its way to the market by slipping through quality control the same way as this lens specimen has. In the latter case, I guess we will soon hear about it.

Soon after introducing the Z8, Nikon published two service advisories asking for cameras with certain serial numbers to be returned for free service. One of these advisories states that the front bayonet of the camera is defective and some lenses cannot be fully rotated within this bayonet and remain unlocked, which sounds familiar to me. Nikon published an online form where one can check one's Z8 serial number for either advisories, and my Z8 is not affected according to Nikon (but my camera had not been made yet, when Nikon published this advisory).

So far the Laowa 85 mm is the only lens that fails to lock on my camera. Everything else I tried, including both Nikon and third-party lenses, adapters and accessories, mounts and locks without problems on my Z8, including some third-party bayonets that look decidedly out-of-specs when visually compared to Nikon-made Z mounts, but work against all odds without blockages or wobbles. Possibly both the bayonet of my Z8 and the one of the Laowa lens are at the limits of their specifications, and only an "unlucky" combination of specific deviations in both mounts causes a physical incompatibility without either mount being outright out-of-specs.

Careful measurements of several Nikon Z lens mounts (from Nikon Z lenses and accessories, as well as third-party accessories), show that the bayonet of the Laowa 85 is about 0.1-0.2 mm thicker (measured from mounting flange to farthest rear point of bayonet) as most of the other Z bayonets. The bayonet of my Nikon Z 24-120 mm is just as thick as the Laowa's, but the chamfer at the end of the bayonet in the Nikon lens is wider, which avoids the problem.

Machining a new chamfer without a machine shop is beyond my abilities, so I decided to grind material from the bottom of the bayonet instead. I removed the bayonet of the Laowa lens, and removed the black metal baffle screwed into the bayonet. I ground the end of the bayonet for a few minutes on a sheet of abrasive paper placed on a flat surface, using circular movements and slightly rotating the bayonet in my hand at regular intervals to avoid an uneven grinding around its perimeter. This removed about 0.2 mm of brass material.

The end of the bayonet is now brass-colored instead of chrome-plated, and the black metal baffle projects by 0.2 mm at the rear of the bajonet, but the lens fits well enough to lock on my Z8.

Optical scheme

I did not see the optical scheme of this lens on the Laowa web site. There is an illustration of the optical scheme on the packaging of the lens, which I took the liberty of copying in the above figure. Unfortunately, this illustration lacks the essential information of which elements and groups are fixed, and which are moved by the focus ring.

By looking at the lens, I can tell that the front doublet is fixed. By comparing the optical scheme with the actual lens, I can also tell that a rear subassembly of four optical elements is fixed, and that focusing moves a third optical subassembly that includes seven elements and the diaphragm. I don't know whether some of the elements in this third subassembly move with respect to each other.

Focus travel is non-linear. The focusing subassembly moves very slowly forward when the lens is focused from infinity to about 2m, then it accelerates rapidly, and moves fastest near 2x. The total rotation of the focus ring is a little less than 180°. More than half of this rotation focuses between ∞ and 0.43 m (i.e. between 0x and 0.25x). This helps to focus with precision in the non-macro range, where a linear movement of the focus subassembly would be too fast and coarse. Focus peaking should be enabled to make it possible to focus with precision without a need to alternate between full and magnified live view.

The aperture ring has click-stops at every full stop. The stops on the aperture ring are unevenly spaced, with a large gap between f/5.6 and f/8 that allows stopping down at roughly one-quarter of a stop intervals, and a very short gap between f/16 (marked only as a dot because of lack of space) and the largely useless f/22. The diaphragm has seven blades.

Lens shade

The illustration of the optical scheme in Figure 3 includes the profile of the lens shade. The mostly-metal lens shade that comes with the lens is cylindrical, 56 mm wide and 30 mm long. It reverses on the lens front for storage, but blocks access to the aperture ring and reduces access to the focus ring when reversed, so it must be either removed or mounted in forward position when using the lens. In forward position, it makes removal of the front lens cap difficult, and it does cast an ominous black shadow on the subject in the macro range.

This lens shade would be suitable for a short telephoto lens faster than the Laowa 85 mm macro, but is a bit too long and too wide for a macro lens, and likely to interfere with illumination of the subject. As I did previously with several other macro lenses, I replaced the original lens shade with my own (Figure 4). This lens shade is proportionate to the diameter of the front lens element and much smaller than the original, is unlikely to interfere with illumination of the subject, "eats" less working distance, causes no vignetting, protects the front element better against accidental touching, and is at least as effective as the original lens shade in preventing flare. It does not reverse onto the lens for storage, but on the other hand it takes very little bag space, and can be left permanently mounted on the lens.

To make this lens shade, I used, from bottom to top:

• a 46 to 37 mm step-down ring
• a 37 to 30 mm step down ring
• a 30 mm lens shade, not too long
• a 37 mm butterfly lens cap (not shown) to mount on the end of the lens shade instead of the original 46 mm front lens cap.

Different names of this lens

The name of the lens printed on the package is an oddity: Mini FF II 85 mm F5.6 Macro 2:1, also repeated at the front of the lens itself together with the filter size, the lens serial number, and the Laowa logo. On the Laowa web sites, the lens is instead called Laowa 85mm f/5.6 2x Ultra Macro APO, but the pictures of the lens do spell out proudly the name Mini FF II 85 mm F5.6 Macro 2:1 printed at the front of the lens, just like in my specimen.

Why two different names? Why the II in the name, which suggests there was a version I of the lens, while there is no trace of a version II of this lens on the web site? Does this oddity have anything to do with the fact that the bayonet on my specimen of the lens is defective, perhaps because it was an early technical sample produced before the commercial lens release? Or perhaps it is just that the Product Development and the Marketing departments of Laowa don't talk to each other, or such departments don't exist and decisions like a lens name are taken by one or another random guy acting alone?

Many questions, no answers. At least, someone at Laowa does know how to design lenses that (generally) work. It is not a given among Chinese lens makers.

Aperture behavior

The effective aperture of an ideal lens determines the amount of light that reaches the sensor. Nominal aperture of a lens is given by the traditional formula

$$\mathit{f}=\frac{\mathit{F}}{\mathit{D}}$$

where f is the nominal aperture, D the diameter of its front element, and F the focal length of the lens. Aperture is usually expressed as an f/ratio. In an aperture scale expressed in this way, each successive full-stop value is represented by the familiar sequence 1, 1.4, 2, 2.8, 4, 5.6, 8 etc., where the next value is calculated as the current value multiplied by $\sqrt{2}$ and rounded to one decimal digit.

With distant subjects, f determines the amount of light that passes through the lens and reaches the sensor. When a lens is used in the close-up and photomacrography range, f is no longer an accurate measure of the transmitted light, which decreases with increasing magnification. In these conditions, effective aperture of a lens is a correct measurement of the aperture of the lens. As a first approximation, the effective aperture relates to the nominal aperture according to the "conventional wisdom" formula:

$${\mathit{f}}_{\mathit{e}}=\mathit{f}(\mathit{M}+1)$$

where f_e is the effective aperture, f the nominal aperture, and M the magnification. When the lens is focused at infinity, effective aperture equals the nominal aperture. When the lens is focused on a subject closer to the camera, the lens moves away from the sensor, and this reduces the amount of light that reaches the sensor. Effective aperture is a measure of this amount of light, and at a magnification of 1x (or 1:1) effective aperture is two stops higher (i.e. double the f/ value) than focused at infinity. In practice, at 1x one-quarter of the light reaches the sensor, compared to focus at infinity). The rest of the light does not magically disappear, but is spread onto a larger focal plane, and in practice is absorbed by the black coating and baffles on the interior of the lens barrel. For each additional unit of magnification, effective aperture increases by one stop, i.e. at 2x effective aperture is three stops more than nominal aperture. Thus, theory tells us that the Laowa 85 mm f/5.6 (where f/5.6 is the nominal aperture) should have an effective f/11 aperture at 1x, and f/16 at 2x.

In a real lens, the effective aperture is determined by a number of factors. If the lens changes focal length when focusing, like internal-focus lenses are well-known to do, effective aperture also changes from the amount predicted by the above formula. Computing the exact focal length of one of these lenses at different focus positions is not trivial, and requires a knowledge of lens parameters not normally published by lens makers.

Pupil ratio and lens speed

Focal length, diameter of the lens and magnification are not the only factors that control effective aperture. Pupil ratio, a.k.a. pupil magnification (see also photomacrography.net), is the ratio of the lens aperture diameter as observed from the rear versus front ends of the lens. Pupil ratio also affects the effective lens aperture. Internal focusing may change the pupil ratio at different focus settings, further complicating things. Fortunately, it is relatively easy to empirically measure the pupil ratio of a lens. Pupil ratio is generally defined as:

$$\mathit{P}=\frac{{\mathit{P}}_{\mathit{out}}}{{\mathit{P}}_{\mathit{in}}}$$

where P is the pupil ratio, P_out is the exit pupil (the apparent diameter of the lens aperture as seen through the rear of the lens), and P_in the entrance pupil (the apparent diameter of the lens aperture as seen through the front of the lens).

Some photographers seem to define pupil ratio as the reciprocal of the ratio given above, i.e. P_in / P_out , so in discussions that involve the pupil ratio it is prudent to make sure that different people are talking of the same thing.

As a rule of thumb, telephoto lenses have a pupil ratio lower than unity, and wideangle lenses a pupil ratio higher than unity. This, however, is not an infallible relationship, and depends on the type of optical scheme of telephoto versus wideangle lenses, rather than their focal length.

In the 85 mm, the entrance pupil (P_in) is essentially unaffected by focusing. P_out , instead, is largest at infinity focus and rapidly decreases as focus moves closer. The pupil ratio of this lens is approximately 0.67 at infinity focus and 0.38 at 2x. This pupil ratio is so different from unity that it cannot be ignored in the calculation of effective aperture. Therefore, the effective aperture calculated on the basis of "conventional wisdom" above needs to be revised as follows:

$${\mathit{f}}_{\mathit{e}}=\mathit{f}\left(\frac{\mathit{M}}{\mathit{P}}+1\right)$$

where f_e is the effective aperture, f the nominal aperture, M the magnification and P the pupil ratio. Assuming a nominal lens speed of f/5.6 (per lens specifications), the effective aperture at 2x with the diaphragm fully open is not f/16 as obtained from the simplified formula, but f/35 as obtained by taking into account also P, a difference of a little over 2 stops. At infinity focus, M / P is zero and effective aperture equals nominal aperture, like in the simpler formula we used initially. However, we are not done yet, because the internal focusing very likely changes F, and therefore f.

A macro lens with an effective aperture of f/35 would be completely useless, but there is an additional aspect that we have not considered, i.e. that the lens may be an 85 mm when focused at infinity, but is likely to have a much shorter focal length in the macro range.

One more problem: The front lens group has a diameter of 27 mm. By applying the f = F / D formula mentioned above, we end up with an f/3.1 lens speed. So where does the f/5.6 lens speed specification for this lens come from? When the lens is focused at 2x, a much smaller optical element with a diameter of 15.2 mm almost touches the rear surface of the front group. At infinity focus, this optical element is deep within the barrel, as far as possible from the fixed front group. If we apply the f = F / D formula to this 15.2 mm element, it gives an f/5.59 lens speed. I think this is the way Laowa calculated the lens speed. In practice, the designers regarded the 27 mm front group as an add-on lens of sorts, and the 15.2 mm element as the front element and limiting aperture of the "real" lens.

At 2x, the utilized portion of the fixed front group has a diameter of approximately 15.2 mm, like the diameter of the optical element located immediately behind. I assume that the whole surface of the front group is utilized when the lens is focused at infinity.

Measuring the (approximate) effective aperture

At this point, we still need to cope with the changing lens focal length at different focus positions. We have no knowledge of this design parameter. It is simple, however, to observe how the light intensity at the focal plane changes with focus. We can measure this (in an approximate way) with the camera's exposure system.

• Configure the camera to display the discrete intervals of exposure time at maximum resolution. In the Z8, this is 1/3 of a stop. This is done with Custom settings menu > b Metering/exposure > b2 EV steps for exposure cntrl > 1/3 EV steps (comp. 1/3 EV). In practice, this setting means that the effective aperture measured with the camera's exposure system can be off by ±1/6 of a stop.
• Set the the camera to A (aperture priority) mode.
• Set the lens focus at infinity.
• Lay down the camera in a steady position, pointed toward a uniformly illuminated surface.
• Stop down the lens to a suitable aperture and/or adjust the illumination intensity if feasible. The purpose is to display a convenient exposure time, easy to use in calculations (i.e. something like 1/40 s)
• Make a note of the magnification set on the lens and the exposure time displayed by the camera.
• Without moving the camera or changing any camera setting, set the lens focus at 0.5x, and repeat.
• Repeat once more at 1x.
• Repeat once more at 2x. We now have four measurement values.

An ideal lens displays a sequence of exposures like:

• 0x: 1/40 s (i.e. 25 ms)
• 0.5x: 1/20 s (i.e. 50 ms)
• 1x: 1/10 s (i.e. 100 ms)
• 2x: 1/5 s (i.e. 200 ms)

each exposure is twice as long as the preceding one. In other words, the lens is "losing" one effective stop of speed at each successive magnification.

I performed this procedure with the Laowa 85, and the sequence is instead:

• 0x: 1/40 s (i.e. 25 ms)
• 0.5x: 1/25 s (i.e. 40 ms)
• 1x: 1/15 s (i.e. 67 ms)
• 2x: 1/10 s (i.e. 100 ms)

The 85 mm is obviously not performing like an ideal lens. At 2x, the actual exposure time is only half the one expected from an ideal lens. This is a good thing, because the lens is behaving one stop faster than an ideal lens at 2x, i.e., starting as a nominal f/5.6 lens at infinity focus, it becomes a nominal f/4 lens at 2x (in practice, effective f/11 instead of effective f/16). This lessens the effects of diffraction. Instead of forcing the photographer to use the lens fully open at 2x and getting a borderline-acceptable amount of diffraction blurring, it gives a choice of stopping down by one stop to get a higher depth of field and possibly a better image quality, or shooting fully open to get a shorter exposure time and minimizing diffraction.

The explanation for the actual behavior of the 85 mm must lay in the fact that the focal length of the lens shortens substantially with the magnification setting. Since the focal length changes with focusing, the nominal aperture of the lens changes with focal length, in addition to magnification. The assumption that the 85 mm remains a nominal f/5.6 at different magnifications is therefore unfounded.

Measuring the change of focal length

While computing the focal length of a modern lens is impossible without a detailed knowledge of the design parameters, it is much easier to empirically measure the focal length of a lens at a given magnification (as set on the lens focus ring), at least in a lens with manual focus. A practical method is described on photomacrography.net. This method requires recording two images of the same measurement target, shot without changing the lens focus settings, and with a different extension between the lens and the camera. One of the extensions can be zero, i.e. the lens can be directly mounted on the camera. Extension is usually obtained by mounting one or more extension rings between lens and camera.

The formula is:

$$\mathit{f}=\frac{\mathit{e}-\mathit{e}\mathbf{\text{'}}}{\mathit{m}-\mathit{m}\mathbf{\text{'}}}$$

where f is focal length, e and e' the extension before and after adding the extension ring, respectively, and m and m' the magnification before and after adding the extension, respectively. The magnification is measured from the test images of the measurement target as m = s' / s, where s' and s are the sizes of the test target in the image and in reality, respectively. Since digital images are dimensionless, the linear size of the subject image projected on the sensor is used as the target size on the image.

The measurement target can be a ruler, millimeter paper or microscope ruler, depending on the lens magnification. For practical reasons, the added extension should be enough to cause a significant change in magnification, albeit not an excessive change (i.e. m and m' should remain of the same order of magnitude).

The target needs to remain the same only in the pair of images shot at a given lens magnification setting. At different lens magnification settings, it is entirely OK to use a different target. This may be necessary when measuring the focal length of a lens at broadly different magnifications.

I decided to measure the actual lens focal length at 0x (i.e. infinity focus), 1x and 2x. For this test I purchased a set of two Viltrox extension rings, 24 and 12 mm long, respectively. Nikon stopped making extension rings for its lenses already at the time of AI lenses. Currently, all third-party extension rings for Z lenses are made of plastic with aluminum bayonets, and very lightly built. I have been unable to find solidly built extension rings for the Z system, and none at all without electric contacts seem to exist.

The procedure in practice:

Test at infinity:

1. Add a 24 mm extension ring between camera and lens.

The above step is necessary because it is not practical to place a measuring target at infinity (or a large distance, e.g. tens of meters). The lens neither knows nor cares that an extension ring has been added at its rear. Image quality may of course be affected because the lens is no longer working at its design parameters, but this is irrelevant in the present test, as long as we can get an image clear enough to read the measuring scale.

I had to use a 24 mm extension ring in this case, because an extension of 12 mm required a focus distance that exceeded the column height of my photomacrography setup.

2. Set the lens at infinity focus (as indicated on the distance scale on the lens barrel).
3. Bring the measuring target into focus by moving it with respect to the camera.
4. Shoot the first test image.
5. Add the 12 mm extension ring to the 24 mm extension ring.
6. Check that the lens is still set at infinity focus.
7. Bring the measuring target into focus again
8. Shoot the second test image.

Test at 1x:

1. Remove the extension rings.
2. Set the lens to 1x magnification.
3. Focus the target as in the test at infinity, step 3, and shoot the first test image.
4. Add the 12 mm extension ring, focus the target again, and shoot the second image.

Test at 2x:

1. Remove the extension ring.
2. Set the lens to 2x magnification.
3. Focus the target as above, and shoot the first test image.
4. Add the 12 mm extension ring, focus the target again, and shoot the second image.

Results

The width of the displayed image on which I performed the measurements is 446 mm, and the width of the active sensor area of the Z8 is 35.9 mm. Based on these measurements, the display magnifies the original image by 12.4x. Accordingly, I calculated the following lens magnifications:

• lens at 0x, 24 mm extension: 0.380x
• lens at 0x, 38 mm extension: 0.419x
• lens at 1x, 0 mm extension: 0.98x (in theory, this should have been 1x, but it is within -2%)
• lens at 1x, 12 mm extension: 1.30x
• lens at 2x, 0 mm extension: 1.93x (in theory, this should have been 2x. It is a little short, but still only by -3.5%)
• lens at 2x, 12 mm extension: 2.38x.

The actual lens magnification with the focus ring set at nominal 1x is close to the expected 1x, and well within the margin of possible measurement error. It falls a little short at nominal 2x, which is at the hard stop of the focus ring and therefore more repeatable than 1x. Both results are actually quite close to the lens specifications. I have seen significantly worse deviations from the nominal magnification in some of the other macro lenses I tested. Nonetheless, in further calculations of the Laowa 85 mm I used the measured magnification.

*** work in progress for the rest of this section ***

This is where I run into trouble with the calculations. If I plug the numbers into the f = (e - e') / (m - m') formula, I obtain nonsense values, especially close to infinity focus. The focal lengths calculated at 1x and 2x seem extremely short, perhaps not compatible with the known working distance of 96 mm at 1x and 69 mm at 2x. These focal lengths would require the entrance pupil to be in the air in front of the lens, but the aperture as seen from the front of the lens lays behind the front element, not in front:

• at 0x: (24 - 36) / (0.38 - 0.419) = 307.7
• at 1x: (0 - 12) / (0.98 - 1.30) = 37.5
• at 2x: (0 - 12) / (1.93 - 2.38) = 26.6

On the other hand, based on the nominal lens speed of f/4 computed from my empirical measurements of exposure times at 2x, and on the 15.2 mm diameter of what the Laowa designers apparently regarded as the front element of the lens when they derived the f/5.6 speed of this lens at infinity (as discussed above), one can compute a focal length of 60.8 mm at 2x, which seems more reasonable.

A shortening focal length while focusing at closer distances is often regarded as a disadvantage by photographers specializing in photomacrography, because every little bit of additional working distance is seen as a good thing in this type of photography (and it often is). When this shortening of focal length is properly used by lens designers to decrease the effective lens aperture at high magnification, as seen in the Laowa 85 mm f/5.6, it is a significant advantage because it reduces the blurring effects of diffraction without requiring costly large-aperture optics.

Of course the gain in lens aperture at close focus is only useful if accompanied by a high image quality with the aperture fully open. It is useless to make (or buy) a faster lens if it must be stopped down one or two stops to produce a sufficiently good image quality. At the high effective apertures typical of photomacrography, forcing the photographer to stop down to reduce aberrations causes a visible increase of diffraction blur, and makes any reduction of non-diffractive lens aberrations a moot point.

Samples

The following samples are 1:1 crops of an area of 900 by 600 pixels, shot at 1x and 2x, respectively, with aperture fully open. The subject is a several years old, slightly worn out laser printout on a macroscopically smooth thin cardboard for high-quality printing. The black matter is laser toner.

The 1:1 crop at 1x is very sharp. It may in fact be difficult to believe that it is a 1:1 pixel crop, instead of a reduced picture of larger original pixel count. The 2x crop is less sharp, still acceptable considering that this is a small part of a 45.7 Mpixel image, but it suggests that the lens is working close to its limit here. Some of the "fuzziness" in the image at 2x is certainly out-of-focus blur, caused by the very shallow DOF and the fact that the subject is slightly three-dimensional. For this reason, I had to select a reasonably sharp area of the image, and Figure 6 corresponds roughly to the lower left quadrant of Figure 5, rather than its center. Effective aperture in Figure 6 is f/11, so diffraction also begins to decrease the image sharpness.

On the other hand, in terms of physical image size, on my computer monitor Figure 6 is displayed at a physical size of 20.8 by 14 cm. The whole image, at the same scale, would be 192 by 128.4 cm. How many practical applications of photography require pixel-peeping an image of this size, or discarding 98.8% of the image pixels and keeping only the 1.2% shown in Figures 5 and 6?

Conclusions

The Laowa 85 mm f/5.6 works on full frame, and gives up a fast aperture in order to achieve a physically small and lightweight 2x lens. This is so far the physically smallest and lightest 2x macro lens in Laowa's large and diverse range of macro lenses, even smaller than Laowa macro lenses for APS-C and Micro 4/3 mirrorless cameras.

The lens barrel is made of metal and feels very solid. All scales and index marks are engraved, and therefore durable (except for the Laowa logo and model name at the front of the lens, which are silk-screened but unlikely to ever be touched during use). This is a fully manual lens. It is designed for mirrorless cameras and cannot be used on DSLRs.

The magnification scale on the focus ring is located farther from the distance index mark than the distance scale in m and ft. This makes it difficult to use this scale to repeatably set a magnification. On the other hand, each marking on the magnification scale has a corresponding marking on the metric distance scale. The latter scale can therefore be used to set the magnification with better repeatability.

The focus ring is less sensitive to rotation in the infinity to 0.5x range, to allow a more precise manual focusing, and increasingly more sensitive at higher magnifications, where the focus ring is typically used to change magnification, rather than focusing.

Pupil ratio of this lens decreases from 0.67 at infinity to 0.38 at 2x. If one assumes a constant focal length throughout the magnification range, the observed pupil ratio should cause an effective aperture of f/35 at 2x and nominal f/5.6. An ideal lens with unity pupil ratio should be effective f/16 at 2x and nominal f/5.6. Empirical measurements on this lens, however, show that at 2x it is an effective f/11 and a nominal f/4, i.e. one stop faster than the nominal aperture at infinity. This results in a lesser amount of diffraction blur than predicted by either theoretical model, and makes this lens especially well suited for use at 1x to 2x, in spite of the low f/5.6 nominal lens speed at infinity.

Working distance is 96 mm at 1x and 69 mm at 2x. While this is adequate for most uses, the actual focal length in the macro range is substantially less than 85 mm. The design of this lens trades some focal length and working distance for a lower effective aperture in the macro range.

This lens is very sharp fully open at 1x, slightly less sharp when used fully open at 2x, but still fully usable at this magnification for the large majority of applications.