Venus Laowa 25mm f/2.8 2.5-5X Ultra Macro,
Laowa provides essentially the same data of effective aperture in the user instructions of the lens, albeit only at nominal f/2.8 (rounded to the first decimal, which makes no practical difference).
On the other hand, if we introduce P in the above formula, we obtain:
E = N (M / P + 1)
This is a more correct formula that gives significantly different results when P is substantially different from unity, like in this case. Applying this formula gives:
A comparison of the two tables shows that the effective aperture values at the same nominal aperture and magnification are quite different, depending on how they are computed.
The question is now whether Laowa's lens designers adjusted the values of the nominal aperture of the lens in the specifications of the lens, in order to take P into account. This would be an unorthodox way of specifying the nominal lens speed, but could make some kind of sense in a lens that does not focus at infinity. The alternative is that Laowa's technical writers simply applied the approximate thin-lens formula when writing the lens documentation, without caring about P and its effects. For the moment, I will not attempt to directly answer this question.
The diameter of the front element of the lens, in a lens that only focuses at magnifications substantially higher than 1x, is not a reliable indicator of lens speed. The 15 mm diameter of the front element, plugged into the formula N = D / F (where N is nominal aperture, D the diameter of the front element and F the focal length) produces f/1.6, far from the nominal f/2.8 specification. This formula does tell us that the nominal lens speed cannot be faster than f/1.6, but it can be slower.
A high diameter of the front element can be a result of multiple design choices, including the need to avoid vignetting and darkened corners at all available magnifications. A front pupil placed in the air in front of the lens is technically possible, and is frequently another factor that requires a larger front element. This, however, does not apply to the present lens, where the front pupil is just behind the front element. Thus, answering the above question is not trivial. In the following discussion, I conservatively use the effective apertures as specified by Laowa, as a worst-case specification.
Working distance is 45 mm at 2.5x and 40 mm at 5x. The relatively narrow (40 mm diameter) front of the barrel helps to illuminate the subject. However, an even narrower front diameter should be possible, and would further help. The main limitation is probably the diameter of the diaphragm housing, which is close to the front element, while the aperture ring could be moved a bit farther to the rear.
The following table shows the approximate field of view, in mm, recorded by this lens on a sensor of a given size (FF = 24x36 mm, APS-C = 18.7x24.9 mm, MFT = 13.5x18 mm). Be aware that there is no "standard" APS-C size, and APS-C sensors can somewhat vary in size among and within camera brands. Although easily computed, this table can be practical to have when setting an initial magnifications to use for a given task.
Robert O'Toole tested this lens at 2.5x and 5x (nominal magnifications), and reported that the actual maximum magnification is 4.82x. In order not to unnecessarily duplicate his test, I am presenting detailed results only at nominal 4x.
The subject of this test (Figure 3) is the tip of the tail of the same subject used for tests of the Laowa 100 mm f/2-8 CA-Dreamer Macro 2x. The cropped detail (Figure 4, 5, 6) is from mid-left to the image center. Image quality at nominal f/2.8 (effective f/14, Figure 4) is good but (as expected) slightly less excellent than with the best lenses at lower magnifications, with finest detail not much larger than one pixel in the areas in best focus. Some of the other areas, however, are blurred because they are out of focus, as a consequence of the low DOF. At nominal f/5.6 (effective f/28, Figure 5), the image is slightly blurred by diffraction, but DOF is significantly higher. Depending on the use of this image and the nature of the subject, an aperture in the interval between f/2.8 and f/5.6 could be the best compromise. At nominal f/11 (effective f/56, Figure 6) the image is significantly blurred and, unless the pixel count is substantially reduced, image quality is too poor in spite of the further increase in DOF.
If a low-resolution image for web publication is all that is needed, nominal f/8 and even f/11 might still be good enough. If the best image quality is required, f/2.8 should be used, probably combined with focus stacking if the subject is even slightly three-dimensional.
Figure 4 shows some axial chromatic aberration (green out-of-focus blobs, especially at the top and at the left of the subject), that becomes much less evident after closing the aperture to nominal f/5.6. This is a larger amount of this type of chromatic aberration than I have seen in other tests of the same lens. The color and relief of this particular subject may be partly responsible for this.
Figures 7-9 are examples of focus stacks at 2.5x and 5x, respectively, on a 42 Mpixel full-frame sensor. The images were recorded on a Sony Alpha 7 II under continuous illumination by two small LED panels placed very close to the subject, and were fused in Zerene Stacker 1.04, a popular program used for this task since 2009 and capable of handling large stacks of hundreds of pictures. The default settings of Zerene Stacker were used (to make comparisons easier, although these settings may not be optimal for all subjects), with just a single manual adjustment performed during the stack processing. No slabbing was used. The individual JPG images of the stack were loaded into Zerene Stacker unedited, straight out of the camera.
At 5x, each pixel corresponds to 0.9 μm on the subject. The nominal f/2.8 lens speed, together with the measured pupil ratio of 1.86 at 2.5x and 1.79 at 5x (see above), allows a diffraction-limited CoC (circle of confusion) diameter of approximately 1.5 pixels at 2.5x and 3 pixels at 5x (i.e., at 5x, details roughly 3-4 μm across). The camera itself is capable of resolving detail of less than 2 pixels in optimal conditions, so the lens is the limiting factor at 5x, while lens and sensor are fairly well matched at 2.5x (considering the lens, simplistically, as diffraction-limited and "perfect" in all other respects).
This lens turns out to be a practical choice for focus stacking. It is not on par with top-of-the-line fixed-magnification objectives like the Mitutoyo M Plan Apo series, but stacks shot at nominal f/2.8 within the nominal magnification range of this lens are quite detailed, even on a 42 Mpixel sensor. The amount of real detail at 5x is clearly higher than at 2.5x, with some, but not much, empty magnification. In particular, the 5x image makes the appearance of the central cap in each setal socket clearer than at 2.5x, and in some places one can even see part of a ring of very fine setae surrounding the socket of large setae, right at the resolution limit of the system. These fine setae are not resolved in the 2.5x image. The semi-transparent, shiny stray fiber with an apparently purple core is also much clearer in the 5x image.
The evaluation of focus stacks is more difficult, and to some extent more subjective, than the evaluation of a single, unprocessed image. The software used to generate the fused image from the individual images composing the stack typically uses two or more alternative algorithms, and each algorithm can be tweaked by changing the values of a number of parameters. Therefore, this software can potentially affect in multiple ways the final appearance of the fused image.
In addition, virtually all stacking algorithms have known weaknesses, most often in the rendering of overlapped features so distant from each other along the depth axis that when one of them is in focus, the other is invisible in the background or foreground blur. Different algorithms may produce different artifacts in these conditions, and techniques are available to give better results in particular situations like this one. Therefore, numerous reservations must be kept in mind when evaluating a focus-stacked image. Nonetheless, it may be useful to see here an example of largely unedited stacks shot with this lens and fused with one of the most popular stacking software.
I processed the same image stack with Helicon Focus 7.6 (not the latest version, but nonetheless the one I have access to) with default settings, and its three stacking methods gave results a little different from Zerene Stacker. With the present stack, I would give the results of Zerene Stacker a slightly better rating, although this may vary with other subjects.
Helicon Focus seems to be developed mainly for relatively large subjects, while Zerene Stacker seems to be most often used in extreme macro and microscopy. Also, Helicon Focus can do a substantial part of its repetitive number-crunching in the GPU, if your computer is equipped with one of the supported, modern graphic cards. From a development point of view, this means that the source code of Helicon Focus, or at least some of its libraries, may need to be updated often to allow an optimal use of the latest GPUs. Zerene Stacker seems to do all its number crunching in the CPU, which is much slower but does not need frequent code updates. If you need to process dozens of large focus stacks on a daily basis, e.g. on a PC in the photography lab of a research institution or museum, the different speed of the two programs may make a significant difference.
Different types of licenses are available for both programs. Fully paid (i.e. non-expiring) licenses of Helicon Focus currently seem to be somewhat more expensive than the corresponding licenses for Zerene Stacker. However, do your own shopping when deciding the purchase of specific stacking software and licenses.
With this lens, color and contrast are good at all magnifications. Color rendering is consistent with the Laowa 100 mm f/2.8 2x., so these two lenses can be used as a set covering the magnification range between zero (i.e. infinity focus) and 5x without significant interruptions. Probably, most of the other Laowa models of 2x macro lenses, especially the ones specified as Apo, are also suitable to complement the Laowa 25 mm f/2.8 2.5-5x (with the likely exception of the original Laowa 60 mm f/2.8 2x).
The necessity of swapping lenses at one point in this magnification range, and the physically very different sizes and working distances of these lenses, make bridging across the "break" in magnification range time-consuming, especially in the field. This is partly compensated by the fact that the Laowa 25 mm, coupled with one of the Laowa 2x lenses, provides a better image quality of both currently available lenses that offer a magnification range between 1x and 5x. In addition, these lenses provide a magnification range that does require lens swapping at 1x, instead of 2-2.5x.
A few specialized lenses, some of them individually even better than the Laowa lenses discussed herein, combined together can provide a reasonably full coverage of the same magnification range. However, each of these lenses typically excels only in a restricted range of magnifications, requiring frequent lens-swapping when changing magnification, and sometimes also color and contrast adjustments in post-processing to better match each other.
The Laowa 25 mm f/2.8 Ultra Macro is a versatile lens providing a good image quality already fully open, in a magnification range from 2.5x to (almost) 5x and at a reasonable price. This magnification range complements the several models of Laowa macro lenses capable of magnification up to 2x, and the magnification gap between 2x and 2.5x is not a significant drawback in practical use of these lenses.