Sourav Pal and Lakshminarayan Hazra, "Ab initio synthesis of linearly compensated zoom lenses by evolutionary programming," Appl. Opt. 50, 1434-1441 (2011)

An approach for ab initio synthesis of the thin lens structure of linearly compensated zoom lenses is reported. This method uses evolutionary programming that explores the available configuration space formed by powers of the individual components, the intercomponent separations, and the relative movement parameters of the moving components. Useful thin lens structures of optically and linearly compensated zoom lens systems are obtained by suitable formulation of the merit function of optimization. This paper reports our investigations on three-component zoom lens structures. Illustrative numerical results are presented.

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${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=2$. The object distance l is expressed in units of the wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 2

Linearly Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.6305

$-1.0762$

0.8944

1.3812

2.4487

${k}_{2}$

$-2.8827$

1.9912

$-2.7889$

$-2.8123$

$-2.9120$

${k}_{3}$

2.0205

2.9589

2.9824

2.9296

3.0000

${d}_{1}$

0.6749

0.1887

0.7488

0.4087

0.1230

${d}_{2}$

0.4174

0.9937

0.5239

0.9421

1.2160

Z

$-0.2460$

0.177

$-0.145$

$-0.057$

$-0.023$

${r}_{1}$

1.471

1.706

$-0.511$

$-0.734$

$-1.755$

${L}_{\text{sys}}$

1.338

1.500

1.492

1.450

1.402

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0131

0.0097

0.0018

0.0007

0.0005

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=3$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 3

Linearly Compensated Zoom Systems^{
}

l

∞

25

20

15

10

${k}_{1}$

1.0918

1.1456

1.1895

0.9599

1.2531

${k}_{2}$

$-4.9902$

$-4.3258$

$-4.8095$

$-4.6532$

$-4.5652$

${k}_{3}$

$-5.0000$

4.9951

4.9902

4.8388

4.9658

${d}_{1}$

0.7844

0.6583

0.6430

0.8267

0.5937

${d}_{2}$

0.7154

0.7556

0.7924

0.5579

0.8503

Z

0.024

$-0.039$

$-0.034$

$-0.063$

$-0.032$

${r}_{1}$

$-2.990$

$-0.900$

$-0.660$

$-0.310$

$-0.230$

${L}_{\text{sys}}$

1.500

1.487

1.492

1.467

1.484

${\mathrm{\Delta}}_{\mathrm{max}}$

0.1088

0.0051

0.0025

0.0009

0.0001

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=5$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 4

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.5989

0.7801

$-0.8739$

$-0.8426$

$-0.9253$

${k}_{2}$

$-1.7909$

$-1.9922$

1.9140

1.8827

1.9785

${k}_{3}$

1.0972

1.3822

1.9922

1.9922

1.9003

${d}_{1}$

0.0577

0.0324

0.2296

0.2279

0.2436

${d}_{2}$

0.8636

0.5073

0.9926

0.9943

0.9926

Z

$-0.350$

$-0.332$

0.230

0.228

0.228

${L}_{\text{sys}}$

1.271

0.8716

1.452

1.450

1.464

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0051

0.0066

0.0080

0.0060

0.0045

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=2$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 5

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.5191

$-0.8475$

$-0.8006$

1.1173

$-0.9413$

${k}_{2}$

$-2.5308$

1.8328

1.7683

3.0000

1.9853

${k}_{3}$

2.0968

2.9648

2.9941

1.4164

2.9941

${d}_{1}$

0.7490

0.2657

0.2662

0.7627

0.2613

${d}_{2}$

0.3463

0.9724

0.9878

0.3484

0.9292

Z

$-0.345$

0.266

0.263

$-0.279$

0.248

${L}_{\text{sys}}$

1.440

1.500

1.520

1.390

1.430

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0123

0.0593

0.0420

0.026

0.0168

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide- angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=3$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 6

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

1.1944

$-0.7059$

$-0.7548$

0.9648

1.1358

${k}_{2}$

$-4.9951$

1.5950

1.6830

5.0000

4.9951

${k}_{3}$

$-5.0000$

4.9951

4.9511

1.2042

2.4597

${d}_{1}$

0.6998

0.2491

0.2402

0.9304

0.8017

${d}_{2}$

0.7727

1.0344

0.9961

0.3373

0.2062

Z

0.024

0.241

0.239

$-0.225$

$-0.186$

${L}_{\text{sys}}$

1.496

1.524

1.476

1.493

1.194

${\mathrm{\Delta}}_{\mathrm{max}}$

0.1821

0.054

0.0361

0.0191

0.0095

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide- angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=5$. The object distance l is expressed in units of the wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Tables (6)

Table 1

Linearly Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.7605

$-0.9936$

0.9233

0.9389

1.3298

${k}_{2}$

$-1.9062$

1.9414

$-2.0000$

$-1.6541$

$-1.9297$

${k}_{3}$

1.2297

1.7714

1.7479

1.9824

1.9785

${d}_{1}$

0.0049

0.1737

0.3895

0.5145

0.3032

${d}_{2}$

0.6524

1.0385

0.3812

0.6529

1.0185

Z

$-0.244$

0.165

$-0.347$

$-0.177$

$-0.082$

${r}_{1}$

1.450

1.690

$-0.890$

$-0.710$

$-1.130$

${L}_{\text{sys}}$

0.901

1.491

1.427

1.470

1.496

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0054

0.0052

0.0034

0.0028

0.0016

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=2$. The object distance l is expressed in units of the wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 2

Linearly Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.6305

$-1.0762$

0.8944

1.3812

2.4487

${k}_{2}$

$-2.8827$

1.9912

$-2.7889$

$-2.8123$

$-2.9120$

${k}_{3}$

2.0205

2.9589

2.9824

2.9296

3.0000

${d}_{1}$

0.6749

0.1887

0.7488

0.4087

0.1230

${d}_{2}$

0.4174

0.9937

0.5239

0.9421

1.2160

Z

$-0.2460$

0.177

$-0.145$

$-0.057$

$-0.023$

${r}_{1}$

1.471

1.706

$-0.511$

$-0.734$

$-1.755$

${L}_{\text{sys}}$

1.338

1.500

1.492

1.450

1.402

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0131

0.0097

0.0018

0.0007

0.0005

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=3$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 3

Linearly Compensated Zoom Systems^{
}

l

∞

25

20

15

10

${k}_{1}$

1.0918

1.1456

1.1895

0.9599

1.2531

${k}_{2}$

$-4.9902$

$-4.3258$

$-4.8095$

$-4.6532$

$-4.5652$

${k}_{3}$

$-5.0000$

4.9951

4.9902

4.8388

4.9658

${d}_{1}$

0.7844

0.6583

0.6430

0.8267

0.5937

${d}_{2}$

0.7154

0.7556

0.7924

0.5579

0.8503

Z

0.024

$-0.039$

$-0.034$

$-0.063$

$-0.032$

${r}_{1}$

$-2.990$

$-0.900$

$-0.660$

$-0.310$

$-0.230$

${L}_{\text{sys}}$

1.500

1.487

1.492

1.467

1.484

${\mathrm{\Delta}}_{\mathrm{max}}$

0.1088

0.0051

0.0025

0.0009

0.0001

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=5$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 4

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.5989

0.7801

$-0.8739$

$-0.8426$

$-0.9253$

${k}_{2}$

$-1.7909$

$-1.9922$

1.9140

1.8827

1.9785

${k}_{3}$

1.0972

1.3822

1.9922

1.9922

1.9003

${d}_{1}$

0.0577

0.0324

0.2296

0.2279

0.2436

${d}_{2}$

0.8636

0.5073

0.9926

0.9943

0.9926

Z

$-0.350$

$-0.332$

0.230

0.228

0.228

${L}_{\text{sys}}$

1.271

0.8716

1.452

1.450

1.464

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0051

0.0066

0.0080

0.0060

0.0045

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide-angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=2$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 5

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

0.5191

$-0.8475$

$-0.8006$

1.1173

$-0.9413$

${k}_{2}$

$-2.5308$

1.8328

1.7683

3.0000

1.9853

${k}_{3}$

2.0968

2.9648

2.9941

1.4164

2.9941

${d}_{1}$

0.7490

0.2657

0.2662

0.7627

0.2613

${d}_{2}$

0.3463

0.9724

0.9878

0.3484

0.9292

Z

$-0.345$

0.266

0.263

$-0.279$

0.248

${L}_{\text{sys}}$

1.440

1.500

1.520

1.390

1.430

${\mathrm{\Delta}}_{\mathrm{max}}$

0.0123

0.0593

0.0420

0.026

0.0168

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide- angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=3$. The object distance l is expressed in units of wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.

Table 6

Optically Compensated Zoom Systems^{
a
}

l

∞

25

20

15

10

${k}_{1}$

1.1944

$-0.7059$

$-0.7548$

0.9648

1.1358

${k}_{2}$

$-4.9951$

1.5950

1.6830

5.0000

4.9951

${k}_{3}$

$-5.0000$

4.9951

4.9511

1.2042

2.4597

${d}_{1}$

0.6998

0.2491

0.2402

0.9304

0.8017

${d}_{2}$

0.7727

1.0344

0.9961

0.3373

0.2062

Z

0.024

0.241

0.239

$-0.225$

$-0.186$

${L}_{\text{sys}}$

1.496

1.524

1.476

1.493

1.194

${\mathrm{\Delta}}_{\mathrm{max}}$

0.1821

0.054

0.0361

0.0191

0.0095

${k}_{i}$, $i=1$, 2, and 3 are the powers of the individual components. ${d}_{j}$, $j=1$ and 2 are the intercomponent separations at the wide- angle position. ${f}_{\mathrm{WA}}=1$. Z is the total component movement. The zoom ratio is $m=5$. The object distance l is expressed in units of the wide-angle focal length. ${L}_{\text{sys}}$ is the system length. ${\mathrm{\Delta}}_{\mathrm{max}}$ is the maximum axial shift of the image plane.