Martin Kemp suggests that Leonardo da Vinci's knowledge of optics and minerals is evident in the representation of the orb in the Salvator Mundi painting (Nature 479, 174–175; 2011). But I question his interpretation that the double contour of the heel of the hand holding the orb depicts the birefringence (double refraction) arising in a calcite orb.
The painting shows no optical distortion in the folds of the clothes, for example, as would be expected from refraction by an orb of calcite, quartz or glass, or even a water-filled glass vessel. In reality, an inverted and nonlinearly reduced image of most of the chest, arm and shoulder would appear within the orb's outline; the heel of the hand would appear in the top half of this image.
An additional image (nonlinearly enlarged and upright) would open up within the inverted first image if part of the hand or cloth were near the central back surface of the orb. Such refractive effects would be more obvious than any due to birefringence in calcite.
The double contour of the hand continues slightly outside the orb, hence it could be due to a previous stage of the painting, or pentimento. The absence of refraction or reflection effects suggests that the orb depicts an idealized celestial sphere, with the painted specks on its surface representing heavenly bodies.
Martin Kemp replies:
As far as we can tell, given the damage to the Salvator Mundi, the garments behind the sphere are indeed undistorted (Nature 479, 174–175; 2011). But it is wrong to assume that Leonardo da Vinci painted all of the optical phenomena he knew about.
No painters at the time depicted such things as the blur of fast-moving objects or the refraction of limbs in water, because that would have been bad pictorial etiquette. The first blurring in a painting is not seen until more than 100 years later, in the work of Diego Velásquez. Leonardo specifically said that such extreme effects are for the speculatori (natural philosophers), not the painters. To show the full effects of the sphere on the drapery behind would have been grotesque in a functioning devotional image.
Contrary to what has become a common belief, Leonardo did not aspire to represent his subjects as if he were a scientist recording natural phenomena. Rather, he was remaking nature synthetically in the functional context of specific paintings (M. Kemp Leonardo revised edition, Oxford University Press; 2011).
The birefringence is a side issue and not important for the attribution. The conservator of the picture cannot tell whether the double heel of Christ's hand is deliberate, a result of damage or a pentimento.