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#005 How Should We Square the Circle, Boss? Microscopy Insights

Author: Emmanuel G. REYNAUD | Lecturer/Assistant Professor | School of Biomolecular and Biomedical Research, University College Dublin, Belfield, Dublin 4, Ireland.

 

PART I – The early days 

While all our lenses, objectives, and other optical elements revolve around the perfect circle and fullness of this organic shape; our pictures, our paintings, and our camera are all bound and framed in angular square shapes. But how do you turn a circular field of view into an optimized square?


The Egg or The Hen, Who Draws First?

It may be obvious to all of us but making round objects is easier than square ones. Many organic shapes lack angles and rolling things in the palms of our hands will produce balls rather than cubes. The first lenses, or quartz-carved objects, like the Nimrud lens, were round. Similarly, the first spectacles were two circular lenses mounted on a frame as we are no Cyclops. Our eyes are spherical balls with a round retina, and a round lens and so our vision world is defined as a sphere we barely can see as one circle.


Contrary to that, the writing world moved from Assyrian empire tablets to the cheaper and more versatile papyrus, which was formatted in a rectangular format, AKA the portrait mode. The collision of these two worlds - visual and writing - and therefore their formats -  round and rectangular, led to some awkward moments when it came to printing the objects observed under newly developed optical instruments in a book format.


The complex problem of squaring a circle or circling a square has led to many theories including the well-known Vitruvian man where Leonardo da Vinci tried to physically wrestle a circle into a square or the other way around. However, due to the size of the required lens or imaging apparatus, this approach is only usable for large telescopes. (Figure 1)



Early attempt by Leonardo Da Vinci to convert a square into a circle with a Gold Number approach


Figure 1 – Early attempt by Leonardo Da Vinci to convert a square into a circle with a Gold Number approach. Leonardo da Vinci, Vitruvian Man (c. 1490). Pen and brown ink with wash over metalpoint on paper (34.4 x 24.5 cm), Gallerie dell’Accademia, Venezia. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 100 years or fewer.







The Antonie Van Leeuwenhoek approach was freer and without the visible boundary of his hand-held instrument with massive aberrations and undefined boundaries (Lane, 2015) he drew his observations without any frames or boundaries (Figure 2).



Yeast drawn by Antonie Van Leuwenhoek

Figure 2- Yeast drawn by Antonie Van Leuwenhoek (Arcana naturae detecta; Editio Novissima, Auctior & Correctior, 1722; https://bibdigital.rjb.csic.es/records/item/13608-arcana-naturae-detecta-editio-novissima) This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 100 years or fewer.


It is interesting to note that Antonie developed his optical instrument using a spherical lens to look at fabric, which are mostly linear and rectangular structures.

Robert Hooke preferred the compound microscope over a single objective lens. Thus, the tube lens has a lens at each end, restricting your vision to a disk. Therefore, many of the illustrations in his fundamental book “Micrographia” are defined by a circle. And one of the first figures of his book is about looking at a ribbon of fabric (Figure 3). How unusual!



Robert Hooke drawings in “Micrographia,

Figure 3 – Robert Hooke drawings in “Micrographia, or, Some physiological descriptions of minute bodies made by magnifying glasses: with observations and inquiries thereupon” https://www.biodiversitylibrary.org/bibliography/904. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 100 years or fewer.

 

Compound microscopes were developed by Hans Lippershey (c. 1570-1619), a Dutch eyeglass maker, and Zacharias Janssen (c. 1580-1638) defined a new space: the tube lens and so framed the microscopic observations within a black frame. Some naturalists still preferred to draw and produce illustrations without a black disk around like the German naturalist Christian Gottfried Ehrenberg (Figure 4).



An illustration by Christian Gottfried Ehrenberg

Figure 4 – An illustration by Christian Gottfried Ehrenberg. Please check the great article by John Dolan and the books freely available at the Biodiversity Heritage Library https://www.openscience.fr/The-Lesser-Known-Scientific-Art-of-Christian-Gottfried-Ehrenberg. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 100 years or fewer.




In the next blog post of Microscopy Insights, I will show you how to fit a circle in a rectangular photographic plate and then chop the corners to finally fit the camera chip into the square, losing data along the way.

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