TITLE: Why zone-plate photography is not monochromatic?
QUESTION [2 upvotes]: Zone-plate photography produces somewhat "blurry" photos. However, according to Fresnel's equation, I'd expect the resulting photos to be somewhat monochromatic, due to the dependence between $r,f$ and $\lambda$:
$$f = \frac{2 r_{N} \Delta r_{N}}{\lambda}$$
i.e. if the rings are "properly" constructed, we'll have a different focal point for different wavelengths, which contradicts the fact that in the photo mentioned above we can distinctly see red, green and blue.

REPLY [1 votes]: (Following @garyp's comment)
We'll indeed have different focal points for different wavelengths:
$$\frac{\partial f}{\partial \lambda}=-\frac{2 r_{N} \Delta r_{N}}{\lambda^2}$$
taking typical values of $r_N \sim 10^{-2}\mathrm{m}$, $\Delta r_N \sim 10^{-3}\mathrm{m}$, $\lambda\sim 5\cdot 10^{-7}\mathrm{m}$, we get:
$$\frac{\partial f}{\partial \lambda} \sim -\frac{2\cdot 10^{-2}\cdot 10^{-3}}{(5\cdot 10^{-7})^2} \sim -\frac{10^{-5}}{10^{-15}} = -10^{10}$$
so $\Delta f \approx \frac{\partial f}{\partial \lambda}\cdot \Delta\lambda$ (where $\Delta\lambda$ is in the order of 100nm) is in the order of $10^{-3}$, i.e. a few millimeters over the whole optical range, which is too small of a difference to cause any monochromatic effect.

You also need to consider depth of focus, which is a little more complicated... the focal spot remains small for a certain range of image distances. – @garyp
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