Historical Questions

Did the technology exist at the start of the Renaissance to produce optics of the necessary quality?

There is ample evidence that not only were suitable optics—both refracting and reflecting—available, but also that they were inexpensive. Tomaso da Modena’s 1352 paintings of ‘Hugh of Provence’ and ‘Cardinal Nicholas of Rouen’ show, respectively, spectacles and a magnifying glass, and ‘Isnardo of Vicenza’and ‘St. Jerome’ both show concave mirrors.

From: Tomaso da Modena, Robert Gibbs (Cambridge University Press, 1989) and Tomaso da Modena, Luigi Coletti (Neri Pozza Editore, Venezia, 1963).

About these mirrors, Robert Gibbs writes in his 1989 book on da Modena that “Isnardo da Vicenza is preparing his office; there is a reading glass (an enlarging-concave-mirror) on the shelf behind him.” Further, in a footnote to that sentence, Gibbs explains “Mirrors, despite their inconvenient habit of reversing the text, were used alongside lenses to enlarge small and faded handwriting.” (note: when properly oriented, concave mirrors magnify the text without reversing it). Gibbs continues in his footnote “The use of mirrors for reading continued into the sixteenth century, and the second (not the first) representation, of a variant type set in a leather horn rather than on a fixed metal stand, appears on St. Jerome’s shelf…”.

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(This shows how easy it is to project a large, bright image of an object illuminated by sunlight using a simple concave mirror) ©2001 BBC Omnibus

David Lindberg’s A Catalogue of Medieval and Renaissance Optical Manuscripts (Pontifical Institute of Medieval Studies, 1974) lists 61 manuscripts written in the years 1000–1425. Contrary to popular perception, this shows the period leading up to the Renaissance was a very active time of scientific activity. Unfortunately, for those of us who do not read Latin, most of these manuscripts have never been translated into English. However, passages that have been translated include:

“…this is the concave surface of a paraboloidal body… The construction of such a surface proceeds as follows. Have a concave cone turned [on a lathe], the larger the better…”
De speculis comburentibus, Roger Bacon, c1260
translated by David C. Lindberg, in Roger Bacon’s Philosophy of Nature (Clarendon Press, 1983)

“What is proposed here can be proven experimentally. Indeed, in an iron mirror color appears weaker because the color of the iron, mingled with the reflected light…weakens the [resulting] reflected color. Make a spherical mirror as before [from clear iron]; smooth and polish its interior along the concave portion of its curvature…”
Perspectiva (Book V), Witelo, c1274~1278
Book V of Witelo’s Perspectiva, translated by A. Mark Smith (Polish Academy, 1983)

“…Witelo went on to describe the actual manufacture of a parabolic mirror out of a concave piece of iron. Two equal parabolic sections were drawn on a rectangular sheet of good iron or steel, and cut out. The parabolic edge of one was sharpened for cutting and that of the other made like a file for polishing. These sections were then used, with some mechanism to rotate them about their axes, to grind and polish the concave surfaces of the piece of iron so that it formed a parabolic mirror. [Witelo] gave an interesting account in [Book X] X.62, p. 454 of an illusion produced by the reflection of the subject’s own image from mist, which he said could be reproduced by mirrors.”
Robert Grosseteste and the Origins of Experimental Sciences
A.C. Crombie (Oxford, 1953)

As these passages show, not only are the tools and techniques for fabricating the necessary spherical—and the even more sophisticated parabolic—concave mirrors described in 13th century manuscripts, so is their use for projecting an image.

As for the cost and availability of quality lenses by the mid-15th century, the historian Vincent Ilardi (Professor Emeritus, University of Massachusetts) located correspondence dated October 21, 1462 between Duke Sforza of Milan and his Ambassador to Florence that answers this (Renaissance Quarterly, vol. 29, p. 345, 1976). In his letter the Duke ordered three dozen pairs of eyeglasses to be made to three different sets of specifications. Based on typical travel time of the mail between those two cities, Ilardi estimated it took “barely a week for the manual grinding and polishing of seventy-two lenses and fitting them into thirty-six frames.” Ilardi also points out that the average cost of 6.8 Soldi the Duke paid for each pair was quite modest, given that it was less than half the average daily wage of 17.2 Soldi that a mason earned at that time. Interestingly, according to the U.S. Department of Labor web site, the average daily wage of a construction worker today is ~$120, and according to a call to Lenscrafters®, a pair of their least expensive glass, custom-ground reading spectacles would cost ~$155, so the relative cost of custom optics 540 years ago was even less than it is today. In his abstract for an invited talk at the 2004 Optical Society of America annual meeting, Ilardi writes “Eyeglasses were cheap, plentiful, and exported by the thousand all over Europe and to the Levant — they were not the expensive vision aids of the clergy, the wealthy, and intellectuals, but they were extensively used by artisans as well.”

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Clip from a 2007 public lecture, ending with the projection of the scene from the window of my 10th floor laboratory. One lens from a pair of spectacles, exactly like the ones van Eyck painted in his c1434 ‘van der Paele altarpiece’, is all that is necessary to project every feature, at the correct magnification and depth-of-field, we have shown to be based on optics (however, circumstantial evidence points to the use of concave mirrors, which maintain the parity of a scene, rather than lenses, which reverse the parity, during the initial period after artists began using optics).

As evidenced by the Tomaso da Modena paintings, the situation was the same for the fabrication of appropriate concave mirrors as it was for refractive lenses, since the necessary glass grinding and polishing technology was no different (nb. glassblowing is an alternative possibility for producing concave mirrors). It is interesting to note that in Jan van Eyck: The Play of Realism (Reaktion, 1991), the art historian Craig Harbison writes “Set into some pilgrims’ medals were small convex mirrors… Pilgrims holding up these mirrors appear in fifteenth-century woodcuts… Van Eyck’s desire to portray a Gothic cathedral in a foot-high panel could well have been stimulated by such mirrors.”

Additional insight into the production of concave mirrors was provided by my colleague in the Optical Sciences Center, Professor José Sasián, who has been following developments since shortly after I became involved with David Hockney (we acknowledged José in our July 2000 ‘Optics and Photonics News’ manuscript for his help in running an optical ray tracing calculation for us). José was elected a Fellow of the SPIE–The International Society for Optical Engineering for contributions to his research specialties that include lens and mirror design as well as optical fabrication. Based on his expertise, some time ago I asked José his professional opinion of how long it would have taken a Renaissance glass worker to make a long focal length concave mirror of the size we calculated Lorenzo Lotto used for his c.1523 ‘Husband and Wife’, i.e., focal length ~54 cm (~21″) and diameter ~2.4 cm (~1″). José’s answer was that it would have taken a craftsman at that time “less than two days” to make such a concave mirror. This is worth mentioning in case anyone thinks the technology for producing the necessary concave mirrors (“mirror lenses”) at the time was any more complex than that needed for eyeglass lenses. It certainly was not.

In fact, it takes far less time to make an appropriate concave mirror than my colleague José Sasián thought, because the mirrors can be made from metal rather than glass, as the passages in the previous section show was known at the time. Metal is much softer than glass, so it requires less time to grind and polish, and when completed a metal mirror reflects light without requiring an additional shiny coating to be applied. As shown on the page linked to the heading of this paragraph, using nothing more than simple abrasives, I was able to hand fabricate a concave mirror in 59 minutes with sufficient resolution for van Eyck to have used to produce his drawing of Cardinal Albergati. However, unlike glass, mirrors made of iron, brass, bronze, silver, etc. all rust or tarnish, in each case forming opaque oxides or sulfides in a matter of years, if not months, if not periodically polished. Because of this, no surviving metal mirror will have optical properties anything like it had 600 years ago.

Why isn’t there any contemporary documentation of the use of lenses?

Thanks to interest in the discoveries reported in David Hockney’s book, we now know there is written documentation. As the answer to the previous question showed, there were 61 manuscripts on optics written in the period between 1000 and the time of van Eyck. Also, Peter Schroeder, Professor of English at California State University, San Bernadino, contacted us to suggest we look at the 13th century work The Romance of the Rose by Guillaume de Lorris and Jean de Meun (translated by Charles Dahlberg; Princeton University Press, 3rd Edition, 1995). Dahlberg says in his Introduction “for nearly three hundred years [The Romance of the Rose] was one of the most widely read works of the French language,” so this was a well known work during exactly the period in question, as well as being widely used in university classes today.

I was amazed to read the description of the properties of images created by what de Meun (the author of lines 4059–21780 in this book) simply calls “mirrors” in the paragraph that starts at line 18163: “…Other [mirrors] make different images appear in different situations—straight, oblong, and upside down in different arrangements…. they make phantoms appear to those who look within. They even make them appear, quite alive, outside the mirror, either in water or in the air…” One couldn’t hope to find textural documentation that was more unambiguous that not only did concave mirrors exist as early as the 13th century, but also that they were being used for projecting images (images that are “upside down” tells us the mirrors were concave—hold a shaving mirror a little too far away and you will see yourself upside down—and images that are “quite alive, outside the mirror” is a beautiful description of the images projected by concave mirrors). De Meun even refers to “those who are masters of mirrors,” which tells us there were specialists in such optical imagery at the time. According to the translator, de Meun wrote those words c1275; over 150 years before van Eyck.

There are too many mirror-related passages in this book to quote them all here, but one other is worth mentioning. In the paragraph starting at line 18247 de Meun tells us, among other things, that he won’t bother giving details about the specific “shapes of mirrors” because “Everything is written elsewhere in a book.” Starting at line 18039 he writes “Alhazen(1)…wrote the book of ‘Optics’… There [the student] will be able to discover the causes and strength of the mirrors that have such marvelous powers…” Also, the fact de Meun mentions oblong images in one paragraph tells us they weren’t limited only to simple convex mirrors at the time; they knew how to fabricate distorted (“anamorphic”) ones to project images with as well.

(1)Abu Ali al-Hasan ibn al-Haytham (known in the West as Alhazen or Alhacen). b.965 Basra d.1039 Cairo. In the early 13th century his seven-volume Kit?b al-Man?zir (Book of Optics) was translated into Latin as De Aspectibus.

Geoffrey Chaucer also mentions Alhacen and the strange properties of certain mirrors in his Canterbury Tales of 1387–1400:

And some much wondered on the mirror’s power,
That had been borne up to the donjon tower,
And how men in it such strange things could see.
Another answered, saying it might be
Quite natural, by angles oddly spaced
And sly reflections thus within it placed,
And said, at Rome was such a one, men know.
They spoke of Alhacen and Witelo
And Aristotle, who wrote, in their lives,
On mirrors strange and on perspectives,
As all they know who’ve read their published word.

A. Mark Smith in his Alhacen’s Theory of Visual Perception writes “That Perspectivist optics was commonly studied in late-fourteenth-century England is suggested by Chaucer’s mention of Alhacen and Witelo in a brief passage on ‘perspective’ in the ‘Canterbury Tales’ (lines 225–234 of the ‘Squire’s Tale’).” Smith also writes that “For example, Alhacen’s ‘De aspectibus’, Witelo’s ‘Perspectiva’, and John Pecham’s ‘Perspectiva communis’ all served as university texts, primarily for the instruction of mathematics within the Arts curriculum.”

Witelo’s Perspectiva is closely modeled on Alhacen’s treatise. Witelo writes “It is possible to set up a cylindrical or convex pyramidal mirror in such a way that one could see, in the air, things outside not in sight.” Although no ‘convex’ mirror can create an image, Witelo provides a lengthy description for creating an image that makes perfect sense for a ‘concave’ mirror. This is the same setup as we used, shown on p. 76 of Hockney’s book. Also, the fact the image Witelo describes above is of something “not in sight” tells us it is a projected image, since a virtual image requires the object to be immediately in front of the mirror, in plain sight.

If artists used lenses, why didn’t any of them write about it?

Although I can only speculate, there certainly are several plausible reasons. Artists who were able to use projected images to produce realistic paintings would have had a significant advantage over those who could not. There would have had little incentive to give away this valuable trade secret to potential competitors. Also, artists earned money by spending their time painting, not writing. In fact, very few artists wrote about any of their techniques.

Why didn’t anyone who posed for a portrait notice the lens and write about it?

To address a question like this I have to speculate rather than being able to rely on optical evidence. However, I can think of a number of plausible reasons, and readers of this FAQ no doubt will be able to think of additional ones. For example, the concave mirror we calculated that Lorenzo Lotto used to aid him in painting certain features on the table covering in ‘Husband and Wife’ was only ~2.4 cm (1″) in diameter. Thus, it would have been quite inconspicuous had anyone else even been in the studio at the time (there would have been no reason for anyone else to be there while he painted the table covering). The lower left photo on page 76 of Secret Knowledge shows the layout of a studio, with the mirror—~4″ diameter in that case—on the partition just behind David’s head. Even with this larger mirror, and even without other items hanging from that partition, such a mirror clearly would not have been very noticeable or noteworthy even if the subject had been looking in its general direction. Also, as I discuss in more detail elsewhere in this FAQ, when I posed for David he worked with my upside down image projected onto his canvas for only two minutes (which, because of the geometry of the projection, was not visible to me; see figure immediately below). Then, after ~2 minutes he reoriented his canvas right side up and did the rest of the work on that portrait in the way we think of artists doing such things, i.e. by looking back and forth between me and the evolving image on his canvas. Hence, if an artist had wanted to deliberately hide his concave mirror from his subject, he would have had to do so for only a few minutes. In any case, there are a number of quite plausible reasons subjects would not have even noticed such concave mirrors, nor thought them noteworthy had they noticed. However, having said that, perhaps in light of Secret Knowledge an historian may discover a relevant note in someone’s 500-year old diary that previously had been ambiguously translated by someone without an understanding of the optical properties of concave mirrors. Assuming there are many such surviving diaries, let alone ones that have been studied.


Adapted from page 76 of David Hockney’s Secret Knowledge.

This photograph from David Hockney’s Secret Knowledge, shows how simple the optical setup is. The image of the “Cardinal” (Brad Bontems) is projected by the concave mirror onto the inside wall beside the window. In this photograph David already has removed the drawing from the wall and is completing it by directly viewing the Cardinal through the window. To later project an enlarged image of the final drawing onto a canvas to help produce a painting would only require placing the drawing in the position where the Cardinal now sits, and placing the canvas on the wall beside the window. Bumping either the drawing or the canvas twice by only ~4 mm (~3/16″) during this process would result in the effects discussed above for van Eyck’s painting.

Did you find any evidence that Leonardo da Vinci used lenses?

Leonardo enters the story a little later in the Renaissance, starting to record his observations and designs in notebooks c1490. Those notebooks include discussions of aberrations from spherical and parabolic surfaces, as well as several designs of machines for fabricating concave mirrors.

Only half of Leonardo da Vinci’s notebooks still exist, but these figures from his surviving notebooks show his interest in the optical properties of concave mirrors as well as in ways to use machines to replace skilled manual labor for their manufacture. In case the captions on the figures are too small to read easily, two of them say “Leonardo’s study made on spherical aberrations of mirrors,” and “Potter’s wheel for making mirrors with large focal length.” Apparently, though, none of his surviving notebooks contain any mention of him having used a concave mirror to project an image. However, in light of these figures alone, coupled with everything else we know about him, it is inconceivable he was not well aware of their imaging properties.

As an aside, we already know from the 1351 paintings of Tommaso da Modena and the c1275 text of The Romance of the Rose discussed elsewhere in this FAQ that concave mirrors had been in use for imaging applications since at least the 13th century. We also know from optical engineers like José Sasián, also discussed elsewhere in this FAQ, that it would have taken skilled optical workers back then a few days to grind and polish the mirrors. We can speculate from these two pieces of information that Leonardo da Vinci’s reason for inventing machines to grind concave mirrors may have been that demand was sufficient to motivate him to think of ways to replace slow manual labor with faster machines. Such machines also would reduce the need for skilled labor, since they would allow unskilled workers to grind the basic concave surface, leaving only the final polishing to skilled craftsmen.

Sadly, though, not only have half of his notebooks been lost, many of his paintings have been lost as well. However, Leonardo certainly is someone who should have known how to project an image onto canvas with either a refractive lens or a concave mirror. He is also someone who would have known better than most how to make best use of such a lens. It is important to realize that where we thus far have been able to discern optical artifacts of the use of lenses within particular paintings, it is because of “mistakes” the artists made when using the lenses (e.g. an out-of-focus feature, changes in vanishing points within straight line segments, etc.). Had those artists not made those mistakes, it is far less likely we would have been able to extract any evidence about the lenses. In any case, if Leonardo da Vinci did use a lens to aid him with any of his still-existing paintings, he was clever enough not to make the small mistakes Campin, Lotto, van Eyck, etc. did, so we have been unable to tell.

Which artists used ‘mirror lenses’ and which used ‘refractive lenses’?

It is only when artists made mistakes—such as Lotto’s problem with depth of field in his ‘Husband and Wife’—that can we extract indirect evidence about the type of optics they may have used. As later generations of artists became more skilled with the use of projected images, they made fewer mistakes. However, circumstantial evidence points to the use of mirror lenses for a century or so after van Eyck, followed by a transition to refractive lenses.

Could a lens be used to help artists make copies of their paintings?

Indeed a lens can. In fact, the identical optical setup is used for projecting a two-dimensional painting as for a three-dimensional person or object. The sub-millimeter accuracy with which van Eyck’s painting of Cardinal Albergati reproduces his 40%-smaller drawing provides very strong evidence that van Eyck used a lens to aid him in making this painting by enlarging the drawing by means of a projection. Evidence of van Eyck’s use of optics is contained in other of his paintings as well. Van Eyck’s drawing of Cardinal Albergati is ~40% smaller than his painting. However, as shown when you roll your cursor over the detail at the right below, when we enlarge the drawing and overlay it on the painting, the correspondence between the major features (eyes, nose, mouth, etc.) as well as the minor details (wrinkles, lines, creases, etc.) within each of the three large regions outlined above is to a precision of better than 1 mm, providing strong evidence that van Eyck used a lens as a tool.

Albergati-CombinedLeft: Full painting (32.5×22.5 cm / 12.8″×10″).

Right: ~7×5 cm (~2.8″×2″) detail of van Eyck’s drawing enlarged by ~40% to match the size of his painting. Roll cursor over the drawing to see that the features match each other to better than 1 mm.

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Two-minute clip by John Shadeck (M.A. student in art education) showing him reproducing the technique Hockney and I proposed van Eyck used to create the high fidelity enlargement of his drawing at a magnification of approximately 40%. As the clip shows, John used a concave mirror (focal length 40 cm) to focus the image of the drawing onto a surface ~40% further away to produce the enlargement. Because of coma and astigmatism, the region of high resolution projected at this magnification by even a high quality concave mirror is fundamentally limited to only a portion of the image, forcing the painting to be pieced together as a composite of four segments.

The Cardinal visited Bruges for four days, 8–11 December 1431, when the daylight in northern Europe is at its lowest. Since the brightness of a projected image scales as the square of the magnification, this ~40% reduction in size of the drawing would have resulted in an image ~2× as bright for van Eyck to work with. Later, when the grey skies and dim light of winter were gone, the same lens and optical setup could be used to enlarge the drawing to the size that the Cardinal presumably had commissioned for the painting. To do this, the drawing would have been placed in the sunlight, rather than the Cardinal, and its enlarged image projected onto the canvas in the identical fashion used to produce the drawing in the first place, as shown in the movie clip above. The four major regions on the canvas are accounted for by the optical setup during this process of producing the enlarged painting.

I read a newspaper article that said a compass could have been used by van Eyck to make accurate copies. If so, why do you say a lens was used?

Several newspaper and magazine articles were based on a press release circulated by one David Stork, who was not involved with the research his press release purported to describe (numerous problems with Stork’s own papers are addressed in a paragraph in Section 9). The actual research by Thomas Ketelsen, Ina Reiche, Olaf Simon and Silke Merchel, based on their discovery of nine pinpricks in van Eyck’s drawing of Cardinal Alberati, was published in the Burlington Magazine (March 2005, p. 170). Unfortunately, there are fundamental problems with this article, including:

  1. The authors found only 9 pinpricks, in only 5 locations, on the drawing. These are far too few to have resulted from someone having used a compass or proportional divider to transfer the sub-mm fidelity of the entire surface of the drawing to the painting.
  2. Ketelsen et al. write themselves that “But the process of transfer, as described here, with an enlargement factor of 1.41, offers no explanation for the greater width of the face as it appears in the painting.” Restating their sentence, the process of transfer they describe (a compass/divider) does not explain the very feature we offered as evidence that optics had been used. As an alternative explanation to optics for the appearance of the painting/drawing, they offer a process that they themselves say does not explain the appearance of the painting/drawing. And, it is not only a “greater width,” that Kettelsen et al. cannot explain with a compass. We offered as evidence of the use of optics the fact the face is composed of four large, offset, areas, within each of which there is very high fidelity between the painting and the enlarged drawing.
  3. Ketelsen et al. write that the drawing was in unknown hands for the 400 years between the time of van Eyck and when it was discovered in 1841, and that it is “much abraded,” “retouched,” “mended by attaching a new piece of paper,” mounted using “an old [cardboard] mounting technique,” and contains a reddish-brown fingerprint that “probably dates from a later period.” Even if somehow those few pinpricks could prove the drawing had at some point been copied using a proportional divider, rather than were made in later times in the course of mending the drawing, mounting it on cardboard, retouching it, abrading it, etc., there is no way to know who in the 400 years prior to 1841 made those pinpricks.
  4. Ketelsen et al. have inadvertently used slightly (2%), but significantly, different magnifications for their overlays of their Figs. 28 and 29, misleading them into saying there is a discrepancy between the underdrawing and the painting. There is no such discrepancy. Also, their 2% error means the “enlargement factor of 1.41,” which caused them to speculate van Eyck used geometry to construct his enlargement, is actually 1.44. An understanding of geometry allows someone to make a construction to give an enlargement of individual measurements by exactly ?2 (1.4142…); not by 1.44.

To summarize, since holes cannot be fingerprinted or carbon dated, there is no way to know who made those pinpricks in the drawing, nor when they made them, nor for what purpose they were made. In any case, they are too few for a proportional divider to be the explanation for the fidelity of the enlarged image on the painting to the drawing even if the painting was a precise enlargement, which it is not; it is composed of four non-orthogonal offset segments, within each of which there is sub-mm fidelity.

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