Near-IR Lens Example

A previous lesson showed how to design an apochromatic objective for use in the visible spectrum. Now we will design one for the near infrared, over the wavelength range from 1.06 to 1.97 um.

Background

The challenge when designing a lens for the infrared is finding optical materials that are useful over the spectral range and whose cost and chemical properties are attractive. The task in this lesson is to redesign an existing lens, replacing some undesirable materials with ordinary optical glass. The reference system is installed in library location 1, with the ID MIT 1 TO 2 UM LENS. (Type PLB to see the current library contents.) You can GET that lens and examine its performance.

That lens has three elements of ZNS and one of AS2S3, making four elements in all. Those names refer to zinc sulphide and arsenic trisulphide glass, and we would like to avoid those materials if possible. The first-order properties we need to match are as follows (dimensions are in mm):

Entering beam radius 17.5

Chief-ray angle 0.935 degrees

Back focus distance 16.3

Cell length 50

The Plan of Action

Rather than try to change the materials in the present lens, all of which have an index greater than 2.0, let us start from scratch. For this we will use the design search program. Here is the input:

DSEARCH 3 QUIET ! the best lens will show up in library location 3 (and also in PAD)

SYSTEM ! system requirements follow

ID NIR EXAMPLE ! lens identification

OBB 0 .935 17.5 ! specify the object

WAVL 1.97 1.53 1.06 ! and the wavelength range

UNITS MM

END

GOALS ! here we set the goals

ELEMENTS 5 ! since glass has a lower index than the present materials, we expect to need five elements.

FNUM 1.428

BACK 16 .1

TOTL 50 .1

STOP FIRST ! there seems to be no reason to let the stop position vary

STOP FIX ! so we put it in front and keep it there

NPASS 10

ANNEAL 200 20

RSTART 10000 ! a rather shallow curve,

TSTART 3 ! and this thickness on each element to start with

END

SPECIAL ! here we give requirements that are not defaults

ACM ! auto edge control (AEC) and center thickness control (ACC) are defaults

ACA ! but we add to these ACM, so thicknesses do not get too thin, ACA,

ASC ! so rays do not approach the critical angle, and ASC so surfaces do not

END ! get too close to the hemisphere point.

GO ! this starts the process.

When this job has finished, we have a very good 5-element lens.

ID NIR EXAMPLE 25772 07-NOV-11 11:50:25

LENS SPECIFICATIONS:

SYSTEM SPECIFICATIONS

______________________________________________________________________________

OBJECT DISTANCE (TH0) INFINITE FOCAL LENGTH (FOCL) 49.9800

OBJECT HEIGHT (YPP0) INFINITE PARAXIAL FOCAL POINT 17.9061

MARG RAY HEIGHT (YMP1) 17.5000 IMAGE DISTANCE (BACK) 16.0486

MARG RAY ANGLE (UMP0) 0.0000 CELL LENGTH (TOTL) 50.0287

CHIEF RAY HEIGHT (YPP1) 0.0000 F/NUMBER (FNUM) 1.4280

CHIEF RAY ANGLE (UPP0) 0.9350 GAUSSIAN IMAGE HT(GIHT) 0.8157

ENTR PUPIL SEMI-APERTURE 17.5000 EXIT PUPIL SEMI-APERTURE 14.3343

ENTR PUPIL LOCATION 0.0000 EXIT PUPIL LOCATION -24.8902

WAVL (uM) 1.970000 1.530000 1.060000

WEIGHTS 1.000000 1.000000 1.000000

COLOR ORDER 2 1 3

UNITS MM

APERTURE STOP SURFACE (APS) 1 SEMI-APERTURE 17.54453

FOCAL MODE ON

MAGNIFICATION -4.99800E-11

POLARIZATION AND COATINGS ARE IGNORED.

SURFACE DATA

_______________________________________________________________________________

SURF RADIUS THICKNESS MEDIUM INDEX V-NUMBER

_______________________________________________________________________________

0 INFINITE INFINITE AIR

APS 57.77402 4.79444 GLM-NdVd 1.63448S 61.54

2 -142.89994 3.08159 AIR

3 66.23033 3.43065 GLM-NdVd 1.63372S 61.61

4 -216.13570 1.68885 AIR

5 -88.99029 2.60031 GLM-NdVd 1.80000S 25.05

6 43.84447 1.00000 AIR

7 23.74938 6.71896 GLM-NdVd 1.62188S 45.70

8 -68.13464 1.07927 AIR

9 -59.37355 25.63459 GLM-NdVd 1.80000S 25.05

10 82.23022S 16.04856S AIR

IMG INFINITE

The index and V-number given in the SPEC listing are the input to the glass model, and they always apply to the CDF spectral lines, which are of course in the visible spectrum. The actual index of each glass (which is the output from the model) will be lower, since we are now in the infrared region. The next step is to change these model glasses into real ones.

The lens is safely stored in library location 3, and for convenience we also save it as a checkpoint in PAD (with the Checkpoint button, ). That way we can try more than one idea and see what works best, always going back to the modeled glasses if necessary.

Open the glass table (with the Glass Table button, in the PAD toolbar) and select the Schott display. This display shows the usual Nd vs. Vd map – but for this case we really want to see the what happens in the near infrared. Click the Graph button, and select the option “Plot P(N3,N2) vs. V(N2)”.

This brings up a different display. Shift-right-click in the display to enlarge it, and you get what is below.

The glass model does a good job of modeling real glasses over the visible spectrum, but just now it wants glass that does not exist for surfaces 5 and 9. Never mind; we have tools that we haven’t used yet.

Remember in the first lesson when we explained that, to get the best color correction, one needs at least three glasses that do not lie on a straight line on the display of the partials? We can apply that trick here as well.

Way over on the left in the above diagram you see two lonely spots that look very attractive. Click on the upper of the two, and the name N-PK51 shows up in the Glass label box. Let’s assign that glass to surfaces 1 and 7, which are strong positive elements. That gives us one corner of our triangle, way to the left. The strongest negative element is at surface 5, so let’s give that the glass N-KZFS2, the spot furthest to the right. The next furthest is higher up, at N-SF66, and we assign that to surface 9. Glass N-SK4 is close to the model for surface 3, so let’s apply that too. Here is our diagram, with those glasses selected:

This is a nicely spread-out selection of glass, and there is a good chance we can correct color this way. So it’s time to reoptimize. Open the MACro DSEARCH_OPT .MAC, which DSEARCH has conveniently constructed for us, and comment out the glass variables so the real glasses are not replaced with new models. Then run the optimization and anneal for a few cycles:

PANT

VLIST RD 1 2 3 4 5 6 7 8 9

VLIST TH 1 2 3 4 5 6 7 8 9

!VY 1 GLM

!VY 3 GLM

!VY 5 GLM

!VY 7 GLM

!VY 9 GLM

END

AANT

AEC

ACC

GSR 0 10.000000 4 2 0.000000

GNR 0 2.000000 4 2 0.750000

GNR 0 1.000000 4 2 1.000000

GSR 0 10.000000 4 1 0.000000

GNR 0 2.000000 4 1 0.750000

GNR 0 1.000000 4 1 1.000000

GSR 0 10.000000 4 3 0.000000

GNR 0 2.000000 4 3 0.750000

GNR 0 1.000000 4 3 1.000000

M 0.160000E+02 0.100000E+00 A BACK

M 0.500000E+02 0.100000E+00 A TOTL

ACM

ACA

ASC

END

SNAP/DAMP 1

SYNOPSYS 20

Wow! This is really good. There is almost no primary or secondary chromatic aberration! We have succeeded in replacing the undesirable materials with ordinary glass, and the performance became much better than the original, at the same time.

Mission accomplished!

Except ... what is the transmission at 2 microns? Type FIND TRANS IN COLOR 1. It comes back 82%. But it’s 96% in the major color, so perhaps this is okay. If not, then go back to the glass map and display the absorption at 1.97 microns – and select glasses with shorter data bars. Lens design is all about tradeoffs, after all, and with these tools one can get the best one rather easily.

If you run this example yourself, you may get somewhat different results. DSEARCH submits each case to the simulated annealing program, remember, and that step involves some randomness. However, the overall quality usually comes out about the same as shown here. If you are adventurous, give it a try! Since this example does not require more than 12 surfaces, you can even run it without a license.