14.1 THE PETZVAL PORTRAIT LENS

14.1.1 The Petzval Design

In designing a Petzval portrait lens it is customary to make both doublets of the same diameter and to mount the stop approximately midway between them. If the front doublet consists of the familiar form with an equiconvex crown, this stop position has the effect of making the tangential field of the front component somewhat backward-curving, and to correct this requires a positive rear component somewhat weaker than the front component. To correct the spherical aberration as well as the OSC and to flatten the tangential field, we find that we must select glass types having a rather large V difference; with the refractive indices used by Petzval, 1.51 and 1.57, a V difference of at least 18 is required. In the present examples the following Schott glasses are used:

(a)Crown: K-1, ne ¼ 1.51173, nF – nC ¼ 0.00824, Ve ¼ 62.10

(b)Flint: LF-6, ne ¼ 1.57046, nF – nC ¼ 0.01325, Ve ¼ 43.05

The V difference is 19.05.

The Front Component

For the front component we adopt a thin-lens focal length of 10 and a clear aperture of 1.8. This aperture may have to be adjusted later after the actual focal length of the system has been determined. For this front lens, the thin-lens formulas give ca ¼ 0.63706 and cb ¼ –0.30618. Assuming an equiconvex crown, our front component is as follows:

0.31853

0.4 1.51173

0.31853

0.12 1.57046

(D – d) 0.086680

Assuming an air space of 2.6, the 10 principal ray enters at Lpr ¼ 2.054 and crosses the axis midway between the two lenses.

The Petzval Rear Component

For a Petzval-type rear component, we may start with the arbitrary Setup that follows:

Extrapolating in the usual way, and because the graphs are remarkably straight, we quickly reach the aplanatic form (Setup D):

with f 0 ¼ 6.2206, l0 ¼ 3.9233, LA0 ( f/3.46) ¼ –0.0009, OSC ( f/3.46) ¼ –0.00003. The fields along the computed 10 principal ray were Xs0 ¼ –0.0597, Xt0 ¼ –0.0123.

To move the fields backward, we must weaken the entire rear component. A few trials indicate that cc should be reduced by 0.025, and after recorrecting the spherical and chromatic aberrations and the OSC we obtain the following solution (Setup E):

with f 0 ¼ 6.4012, l0 ¼ 4.0408, LA0 ( f/3.56) ¼ 0.0030, LZA ( f/5) ¼ –0.0021, OSC ( f/3.56) ¼ –0.00002, Ptz (10) ¼ 0.0811. The results are shown in Table 14.1. These aberrations are plotted in Figure 14.2.

The final check on our system is made by drawing a meridional ray plot at 10 obliquity, which is shown in Figure 14.3a. The abscissas are the height of each ray at the stop with the height of the marginal ray at the stop being shown on the graph ordinate. However, because of vignetting at the front and rear surfaces,

Table 14.1

Astigmatism and Distortion for Setup E

Figure 14.3 Ray plots for Petzval objectives at 10 : (a) Ray plot with rear elements in close contact; (b) Ray plot with air-spaced rear elements.

which are assumed to have a free aperture of 1.8, only a part of the graph is valid. The upper and lower vignetted rays are indicated by VV, whereas the limiting rays through the top and bottom of the stop are marked SS on this graph. It should be noted particularly that the middle of the curve is straight and level as a result of the good correction of OSC and the flat tangential field at 10 , but