Explore the captivating world of large format lenses, where legendary names like Super Angulons, Symmars, and Grandagons tell the story of decades of optical innovation. Discover how these marvels from Schneider-Kreuznach, Rodenstock, Nikon, and Fujifilm contribute to the striking and unique beauty of large format photography.

## Introduction

There is an extensive literature on large format lenses, covering the history of the designs, the types of lenses and shutters, the purpose of the most common focal lengths and lots of technical specifications.

At the beginning of this adventure it was a daunting matter, populated by mysterious and ghostly denizens called Super Angulons, Symmars, Sironars, Grandagons, Fujinons, Nikkors, Super Symmars, Clarons, Ronars, Tele-Xenars and so on… I felt like I was lost in a dark and deep forest, but I was very motivated to learn more about them. After all, they are one of the main reasons why large format photographs are unique and so striking. These marvels of optics were the result of decades of experimentation, optical design and manufacturing, essentially by the big four: Schneider-Kreuznach, Rodenstock, Nikon and Fujifilm.

The following resources have been extremely useful to me in my learning, for consultation and to gain new insights:

- Using the View Camera by Steve Simmons (Rev. Ed). Introductory book.
- The famous “Future Classics” from Kerry Thalmann
- On landscape: Large Format Lenses – The Standards by T. Parkin and R. Childs
- View Camera Technique (7th Ed.) by Leslie Stroebel.
- Applied Photographic Optics by Sidney E. Ray

## Statistical Insights

My analysis is based on the dataset compiled by Michael K. Davis, hereafter denoted as **MKD45**. This data set was essential when I was looking into the details of these lenses to figure out which lens to buy. The most important selection criteria I chose for the search were: focal length [mm], image size [mm], coating type (i.e., none, Multicoating, or EBC), apochromatic (APO, yes/no), weight [g], need for a centre filter, and price [€]. If we visualise this dataset by plotting each selected variable against each other we get Fig.1. This figure shows that a number of variables correlate with others (as expected), but further analyses is required to derive some insights.

When I first saw the MKD45 dataset, I start wondering if someone had made some statistics with it. For example, an histogram with distribution of focal lenses, one with the top manufacturer of LF-Lenses, etc. Then, other more elaborate questions occurred to me:

- Who was the most prolific manufacturer of LF-lenses.
- What was the distribution of focal lengths in this data set?
- Are there specifications contained in MKD45 (also known as predictors in statistics) and straightforward relationships (or functions) that can explain both the quoted price and the size of the image circle?
- What characteristics make Thalmann’s Future Classics unique?
- How does a classification that combines many features from MKD45 (i.e., multivariate) look like?

So far I have not found a synthesis that is related to this dataset. For this reason and because I want to know if there are answers to my questions, I decided to play with this dataset for some time. I hope it is also interesting for other LF photographers.

For this purpose, I used several R packages, including: *Hmisc, ggplot2, ggrepel, visreg, hier.part, dplyr, ggtext, randomForest, quantregForest, neuralnet, np, plotly, combinat, k-means, boot, *bootstrap. The scripts and an ASCII file with the curated MKD45.csv dataset (corrections of some values, filling of missing data etc.) can be found in my Git repository.

## Manufacturers, Focal length and Image Circle

Fig.2 shows that 60% of 4×5 lenses were produced by German manufacturers, of which Schneider-Kreuznach has the largest share (33%). The two Japanese manufacturers had an equal share of 20% each.

The focal lengths are not evenly distributed either (Fig. 3). If we divide the lenses into four classes (based on Simmons): Wide angle (45-125 mm), standard (125-180 mm), long (180-300 mm) and very long (300+ mm), then the frequencies of these classes are 34%, 20%, 30% and 36%, respectively. Consequently, the standard lenses were produced the least frequently than the others classes. Wide angle and long lenses were purchased very frequently as they were usually considered suitable for architectural shots (wide angle) and the long lenses for general work, studio work on the table, portraits in the studio and landscape shots. Very long lenses and telephoto lenses were used for art photography, nature and wildlife photography.

In optics, the image circle is the diameter of the circle formed by a lens in which the image is focussed on a distant object. The size of the image circle depends on several factors, including the focal length of the lens, the aperture and the particular design related with the intended use (e.g. portraiture, landscape, architectural, etc.).

The image circle of modern 4×5 lenses is also quite skewed (Fig.4). The most common value is around 210 mm, the maximum value is over 600 mm, which corresponds to the the amazing Fujinon C. The smallest image circle is 145 mm that belongs to the Schneider-Kreuznach APO-Symmar 100 mm. This lens does not even cover a 4×5 film. I wonder what kind of films and cameras it was made for? Likely barely covers a 9×12 cm film in a 4×5 view camera.

This illustration also shows that Fuji achieved excellent results with lenses that have very large image circles but weigh much less than their counterparts.. This will become even clearer in the next illustration.

## Factors Explaining the Image Circle

The relationship between focal length [mm] and image circle [mm] of all lenses contained in the MKD45 data set is depicted in Fig.5. In order to be able to include telephoto lenses in this graph, I have used the bellows draw instead of the focal length for this kind of lenses. According to Simmons, the bellows draw is about two thirds of the focal length (I used this rule of thumb because I don’t have data from several lens) . The image circle can be roughly estimated as a constant (say 1.5 for simplicity) times the focal length. This theoretical relationship is also shown with a orange dotted line as a reference.

The legend of the Fig. 5 shows the natural logarithm of the weight of the lens. Green colours stand for a light lens, blue colours for a heavy lens.

This illustration clearly shows the enormous variability of the image circle depending on the design of the lens, and this in turn is implicitly related with its weight.

Fig. 5 also shows niches that manufacturers have found to create a specialised product, as in the case of the Fujinon SW (data correspond to the NSW) 105 f/8 (see greenish dot with red square). NSW is one of the few wide-angle lenses with a focal length of 105 mm, but with an extremely large image circle.

The other red squares also show the focal lengths I chose for my equipment: 75 mm, 150 mm,

210 mm, 300 mm and 500 mm. I found that this sequence provides a good transition for my photographic interests.

The next step would be to try to use other specifications provided in MKD45 to be able to estimate the image circle. The search for an optimal empirical relationship will make it possible to answer one of my questions and learn something about these optical wonders.

## The Theoretical Relationship of the Image Circle

Theoretically, the diameter of the image circle at f/22 (*d *[mm) is linked to the focal length (*f* [mm]) and the angle of coverage (α [rad]) by the following equation: *d = 2 f tan(α/2)*. Applying this equation to the data provided in MKD45 we can obtain the green triangles depicted in the in Fig. 6 . These theoretical values show excellent agreement (r2=0.9988) (blue dots) with the data of the image circle available in the data set. It is known that the total image circle also depends on the construction of the lens, thus the small deviations between the actual and the theoretical value can be attributed to the respective constructions. A correction of the theoretical values can be performed with a lens-depended factor *k*, namely *d = 2 k f tan(α/2)*. *k* can be modelled as a potential model that can be estimated as follows: *k* = x_{1}^{b1} … x_{n}^{bn}.

In a first step, the most likely predictors for k (those with the lowest cross-correlation to each other) were selected from the MKD45 dataset. The selected predictors for the correction factor are the following specifications:

- Maximum aperture (
*maxF*=*x*_{1}) - Minimum aperture (
*minF*=*x*_{2}) - Tilt degree landscape (
*tilDl*=*x*_{3}) - Weight [g] (
*W*=*x*_{4}) - Filter size [mm] (
*filS*=*x*_{5}) - Apochromatic (1=T/0.01=F) (
*APO*=*x*_{6})

With 6 potential predictors, there are 63 combinations of potential models. All possible models were automatically generated and their efficiency assessed using the AIC metric. The lowest AIC value indicates the best model.

The theoretical-corrected model is shown in Fig. 6 (best fit). The selected predictors were: * maxF, minF, aCur, W*, and *APO*. This model has a very high coefficient of determination (r^{2}=0.9991), marginally better than the theoretical equation. For practical applications the theoretical equation is consequently enough. The high level of agreement indicates that the MKS45 dataset is fully consistent with the theory. The remaining errors could be due to the truncation of decimals in the data supplied by the manufacturers. The yellow points obtained with the corrected theoretical model are almost above the orange line, which indicates a perfect match between the actual and predicted image circle.

This result clearly answers my third question.

## Factors determining the Quoted Price

The first step was to select the most likely predictors having the least cross-correlation with others. Then they were normalize them in the interval (0,1]. This facilitates the convergence of the parameter optimization algorithms in R. Initially, three types of models were considered plausible: 1) multilinear (*y* = *b _{0} + b_{1}x_{1}+… +b_{n}x_{n}*), 2) exponential with a multilinear exponent (

*y = exp*), potential (

^{b0 + b1x1+… +bnxn}*y = b*).

_{0}x_{1}^{b1}…x_{n}^{bn}The selected predictors to model the quoted (*Price* = y [*US$ 2002]*) are the following specifications:

- Focal length [mm] (
*fLen*=*x*_{1}) - Maximum aperture [f-stop] (
*maxF*=*x*_{2}) - Minimum aperture [f-stop] (
*minF*=*x*_{3}) - Image Circle [mm] (
*iCirc*=*x*_{4}) - Tilt degree landscape (
*tilDl*=*x*_{5}) - Angle of coverage [deg] (
*aCvr*=*x*_{6}) - Weight [g] (
*W*=*x*_{7}) - Filter size [mm] (
*filS*=*x*_{8}) - Apochromatic [-] (1=T/0.01=F) (
*APO*=*x*_{9})

With 9 potential predictors, there are 511 combinations of variables. All possible models for the three types of model structures were created automatically and their efficiency was evaluated using the AIC metric. The lowest AIC value indicates the best model. This procedure was repeated for all model structures. The best models for the three selected structures are shown in Fig. 7.

A jackknife cross-validation technique was used to test the robustness of the best models for each structure. The Jackknife root mean square error (jRMSE) for these models was: 607, 400 and 486 [US$ 2002], respectively. The lowest root jRMSE) correspond to the exponential-multilinear model.

There is a large variability for lenses priced below US$3000 (2002 prices). These prices do not reflect current retail prices, which are mainly driven by “recommendations” increase the demand and short supply (almost 2nd market). It would be interesting to survey the current prices for these lenses (on Ebay) and see how these models have performed. The 2002 US dollars can be adjusted for inflation to get an idea of how much these lenses may cost at current US$.

My interest with this empirical analysis was to get insights on which factors were driven the 2002 prices. In case of the exponential model the selected predictors are the usual suspects: *fLen, minF, iCirc, W*, und *filS*. Interestingly, APO did not appear among the best predictors. If someone would like to try, here the coefficients of the model (*b _{0}*,…

*,b*are 2.59e2, 3.05e-4, 8.76e-3, -1.62e-3, 2.51e-4, 1.74e-2, respectively).

_{6}The exponential model has a very high coefficient of determination (*r ^{2}* = 0.89). The results of the cross-validation show that most of the coefficients are significant. The unexplained variability (deviation from the mean) indicates advantages or disadvantages of the respective lenses.

## How special are Thalmann's Future Classics?

Tim Parkin and Richard Childs, referring to Kerry Thalmann’s famous “**Future Classics**“, have clearly pointed out a dilemma I have when choosing large format lenses. They posed the question, *“These lenses are all very, very good, but do they deserve the price premium they have inevitably gained?* They’re not sure, and neither am I. Based on selections like Thalmann’s (driven by experience, needs, aesthetics, etc.), of course, we don’t know. You need objective criteria based on facts. Parkin and Richard Childs also rightly remarked that the only thing we can be sure of is that this famous list “*probably single-handedly doubled the price of every lens listed*“.

For this reason, I decided to provide some insight into this dilemma by performing the following statistical test. In the histograms shown in Fig. 8, I plot the deviations from the “mean” of a particular feature for all lenses included in MKD45. If a subgroup (e.g. Thalmann) has particular characteristics, then the selection should appear at the ends of the distribution. If this is not the case, one can conclude that its selection is not special with respect to this feature. It is very simple.

The following five characteristics were chosen for carrying out this tests: weight, quoted price, image circle, and two efficiency ratios: image circle and weight per focal length, respectively.

The result of the tests are shown in Fig. 8. Without getting into statistical rigour, it can be concluded that the main criterion to make this famous list was weight.

In summary, the primary criterion behind Thalmann’s “Future Classics” is lens **weight.** Most of the lens in this selection have the least weight per focal length. As can be seen in Fig. 8, this selection does not significantly outperform any other features.

From the literature, it appears that no other sophisticated statistics derived from MTF curves were used for this selection (MDK45 does not have them). After seeing these results, I was amazed at how much fuss was made about this selection.

If you have money, the Future Classic selection is a good investment (as noted by Parkin and Childs), thanks to the speculation this list has generated over the past two decades. If you’re like me, you make your own choices and that’s fine because all of these lenses are already of exceptional quality. More important are the specs you need for your intended use, the physical state of the lens and the retail price.

## Classifying 4x5 Lenses: A Detailed Exploration

There are dozens of classifications of LF lenses. Mine differs from all the others because it is based on the all the information contained in MKD45 (i.e., it is multivariate). The *k-means* algorithm with all (normalised) features contained in this data set was usewd for this task. All variables have equal weights. Ten classes were opted for to allow identification of subclasses within the classical classifications (wide, standard, long). One lens, however, stands as a class of its own: the APO-Tele Xenar TM.