Further Reading

I recommend the seven books below for someone wishing to begin looking deeper into this topic:

  • David Hockney by David Hockney, Nick Stangos, editor (Abrams, 1976)
  • That’s the Way I See It, David Hockney (Thames & Hudson, 1993)
  • Secret Knowledge, 2nd edition, David Hockney (Viking Studio, 2006)

The first two provide details of David Hockney’s life-long interest in the process of making images. As will be clear from these books, Secret Knowledge was the end result of a decades-long quest to understand the appearance of certain features in various paintings.

  • The Manual of Close-Up Photography, Lester Lefkowitz (Amphoto, 1979)
  • View Camera Technique, 7th edition, Leslie Stroebel (Focal, 1999)

The optics-based paintings addressed by our work are composite images containing elements that are of relatively high magnification (e.g. most portraits have magnifications M~0.5–1). This is a regime of image projection that very few people have practical experience with (e.g. a full-length photo of someone reduces a scene that is ~2m/6ft. tall onto a piece of film or a CCD sensor that is ~2cm/1in. high, i.e. M~0.01). Images projected at such high magnifications have very shallow depths-of-field, and typically involve shifts and tilts of the canvas with respect to the lens, which in turn affects perspective, vanishing points, the plane of maximum depth-of-field, etc. These two books provide the technical background necessary for understanding the relevant properties of projected images of the type addressed by our work.

  • The Science of Art, Martin Kemp (Yale, 1990)

This book is an excellent introduction to the historical development of perspective and other aspects of the relationship between art and science. The author is an art historian who was very helpful in aiding Hockney place his visual insights in historical context. However, like essentially all other historians, Kemp was unaware at the time of the imaging properties of concave mirrors. This is seen in his correspondence of 28 September 1999 (reprinted in Secret Knowledge): “However, mirrors cannot be used for practical acts of picture-making in the same direct way as lens- and prism-based devices.” Hockney and I bringing the imaging properties of concave mirrors to the attention of scholars in the humanities has resulted in historians making new discoveries that continues to this day.

  • Color and Light in Nature, 2nd edition, David K. Lynch and William Livingston (Cambridge, 2001)

Although not closely related to our work, this book illustrates and explains a wide variety of optical phenomena in the world around us. Although some of these phenomena are directly relevant to our work, more important is how this book provides insights into the many complex ways light manifests itself in nature.

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