Abstract

Laser collimation is an essential part of many experimental setups including optical coherent processors, image transformers, Fourier transform generators, and 4f-based optical systems. A device is required to test the collimation of lasers in such experiments. We are proposing a modification in the existing two-lens-system (TLS)-based collimation testing technique in which a combination of a convex and a concave lens is placed in space between the collimating lens and the first grating of the conventional setup. In the proposed method, we change the position of the second TLS component, placing it between the two gratings. The proposed idea not only reduces the size of the system but also gives improved results. Theoretical modeling and simulated and experimental results are presented to support our idea.

© 2012 Optical Society of America

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References

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    [CrossRef]
  6. C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).
  7. D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–473 (1997).
    [CrossRef]
  8. C. Shakher, S. Prakash, D. Nand, and R. Kumar, “Collimation testing with circular gratings,” Appl. Opt. 40, 1175–1179 (2001).
    [CrossRef]
  9. R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
    [CrossRef]
  10. S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 1–6 (2007).
    [CrossRef]
  11. L. M. Sanchez-Brea, F. J. Torcal-Milla, F. J. Salgado-Remacha, T. Morlanes, I. Jimenez-Castillo, and E. Bernabeu, “Collimation method using a double grating system,” Appl. Opt. 49, 3363–3368 (2010).
    [CrossRef]
  12. J. Dhanotia and S. Prakash, “Collimation testing using coherent gradient sensing,” Opt. Lasers Eng. 49, 1185–1189 (2011).
    [CrossRef]
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    [CrossRef]
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

2011

J. Dhanotia and S. Prakash, “Collimation testing using coherent gradient sensing,” Opt. Lasers Eng. 49, 1185–1189 (2011).
[CrossRef]

2010

2007

S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 1–6 (2007).
[CrossRef]

2002

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

2001

1997

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–473 (1997).
[CrossRef]

1995

C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).

1994

1993

1991

1987

1971

Bernabeu, E.

Bolognini, N.

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

Butt, S.

Chang, C. W.

Chang, C.-W.

C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).

Chang, D.-Ch.

C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).

Chang, J.-T.

C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).

Chung, P. S.

S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 1–6 (2007).
[CrossRef]

Dhanotia, J.

J. Dhanotia and S. Prakash, “Collimation testing using coherent gradient sensing,” Opt. Lasers Eng. 49, 1185–1189 (2011).
[CrossRef]

Ganesan, A. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Jimenez-Castillo, I.

Kandpal, H. C.

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–473 (1997).
[CrossRef]

Kothiyal, M. P.

Kumar, R.

Mehta, D. S.

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–473 (1997).
[CrossRef]

Morlanes, T.

Mudassar, A. A.

Nand, D.

Prakash, S.

J. Dhanotia and S. Prakash, “Collimation testing using coherent gradient sensing,” Opt. Lasers Eng. 49, 1185–1189 (2011).
[CrossRef]

C. Shakher, S. Prakash, D. Nand, and R. Kumar, “Collimation testing with circular gratings,” Appl. Opt. 40, 1175–1179 (2001).
[CrossRef]

Salgado-Remacha, F. J.

Sanchez-Brea, L. M.

Shakher, C.

Silva, D. E.

Sirohi, R. S.

Sriram, K. V.

Su, D. C.

Tagliaferri, A.

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

Tebaldi, M.

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

Torcal-Milla, F. J.

Torroba, R.

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

Venkateswarlu, Putcha

Zhao, S.

S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 1–6 (2007).
[CrossRef]

Appl. Opt.

Chin. J. Phys.

C.-W. Chang, D.-Ch. Chang, and J.-T. Chang, “Moiré fringes by two spiral gratings and its applications on collimation tests,” Chin. J. Phys. 33, 439–449 (1995).

Opt. Commun.

R. Torroba, N. Bolognini, M. Tebaldi, and A. Tagliaferri, “Moiré beating digital technique to collimation testing,” Opt. Commun. 201, 283–288 (2002).
[CrossRef]

S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 1–6 (2007).
[CrossRef]

Opt. Laser Technol.

D. S. Mehta and H. C. Kandpal, “A simple method for testing laser beam collimation,” Opt. Laser Technol. 29, 469–473 (1997).
[CrossRef]

Opt. Lasers Eng.

J. Dhanotia and S. Prakash, “Collimation testing using coherent gradient sensing,” Opt. Lasers Eng. 49, 1185–1189 (2011).
[CrossRef]

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of modified optical system for collimation measurement [13].

Fig. 2.
Fig. 2.

Collimating components: (a) collimation condition set up by lens1 and lens2 when separated by the sum of focal lengths, (b) uncollimation condition when the two lenses are separated by f1+f2+d, and (c) uncollimation condition when the two lenses are separated by f1+f2d.

Fig. 3.
Fig. 3.

A compact collimation testing technique based on modified TLS.

Fig. 4.
Fig. 4.

Three collimation testing techniques with approximate dimensions: (a) conventional technique, (b) TLS technique, and (c) modified TLS technique.

Fig. 5.
Fig. 5.

Sensitivity comparison of conventional, TLS, and modified TLS techniques in terms of the number of fringes versus the collimating lens position. Continuous solid curves are the theoretical results whereas the solid dots correspond to experimental data. Each dot corresponds to an integer number of moiré fringes.

Fig. 6.
Fig. 6.

Results obtained using conventional collimation testing technique shown in Fig. 4(a) employing sinusoidal gratings. Distance shown under each image indicates the position of the collimating lens2 shown in Fig. 2. Negative and positive displacement shows the displacement of the collimating lens towards the left (diverging beam case) and the right (converging beam case), respectively. Images were recorded at integer numbers of fringes for both diverging and converging beams.

Fig. 7.
Fig. 7.

Results obtained using TLS collimation testing technique shown in Fig. 4(b) employing sinusoidal gratings. Distance shown under each image indicates the position of the collimating lens2 shown in Fig. 2. Negative and positive displacement shows the displacement of the collimating lens towards the left (diverging beam case) and the right (converging beam case), respectively. Images were recorded at integer numbers of fringes for both diverging and converging beams.

Fig. 8.
Fig. 8.

Results obtained using modified TLS collimation testing technique shown in Fig. 4(c) employing sinusoidal gratings. Distance shown under each image indicates the position of the collimating lens2 shown in Fig. 2. Negative and positive displacement shows the displacement of the collimating lens towards the left (diverging beam case) and the right (converging beam case), respectively. Images were recorded at integer numbers of fringes for both diverging and converging beams.

Fig. 9.
Fig. 9.

Results obtained using modified TLS collimation testing technique shown in Fig. 4(c) employing square-pattern gratings. Distance shown under each image indicates the position of the collimating lens2 shown in Fig. 2. Negative and positive displacement shows the displacement of the collimating lens towards the left (diverging beam case) and the right (converging beam case), respectively. Images were recorded at integer numbers of fringes for both diverging and converging beams.

Fig. 10.
Fig. 10.

Plots of visibility versus the number of moiré fringes for the conventional with sine-wave grating, TLS with sine-wave grating, modified TLS with sine-wave gratings, and modified TLS with square-wave gratings techniques.

Equations (24)

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αi=df2σ.
No. of moiréfringes=2·μ·z·Tan[|±αi|]L+2z·Tan[±αi],
z=2λ·μ2,
faL3=Exp[ik2f3(x2+y2)],
faG1=Exp[ik2f3(x2+y2)]·12[1+m·Cos(2πxL)]y,
I{faG1}=(i·λ·f3.Exp[i·π·λ·f3(fx2+fy2)]){12δ(fx,fy)+m4δ(fx1L,fy)+m4δ(fx+1L,fy)}=iλ·f32Exp[i·π·λ·f3(fx2+fy2)]im·λ·f34Exp[i·π·λ·f3{(fx1L)2+fy2}]im·λ·f34Exp[i·π·λ·f3{(fx+1L)2+fy2}].
H1(fx,fy)=ei·k·z1·Exp[i·π·λ·z1·(fx2+fy2)].
I{fbL4}=ei·k·z1{iλ·f32Exp[i·π·λ·f3(fx2+fy2)]im·λ·f34·eiπ·λ·z1L2Exp[i·π·λ·f3{(fx1L)2+fy2}]im·λ·f34eiπ·λ·z1L2Exp[i·π·λ·f3{(fx+1L)2+fy2}]}.
fbL4=12Exp[i·πλ·f3(x2+y22z1·f3)][1+m·eiπ·λ·z1L2·Cos(2π·xL)]y.
faL4=12Exp[i·πλ(x2+y2)(1f31f4)]·ei2πλz1[1+m·eiπ·λ·z1L2·Cos(2π·xL)]y.
I{faL4}=12ei2πλz1I{Exp[i·πλ(x2+y2)(1f31f4)]}I{[1+m·eiπ·λ·z1L2·Cos(2π·xL)]y}=iλ2(f3f4f4f3)·Exp[i·π·λ·(f3f4f4f3)(fx2+fy2)]iλ·m4(f3f4f4f3)·eiπ·λ·z1L2Exp[i·π·λ·(f3f4f4f3){(fx1L)2+fy2}]iλ·m4(f3f4f4f3)·eiπ·λ·z1L2Exp[i·π·λ·(f3f4f4f3){(fx+1L)2+fy2}].
H2(fx,fy)=ei·k·z2·Exp[i·π·λ·z2·(fx2+fy2)].
fbG2=ei2πλ(z1+z2)I1{iλ2(f3f4f4f3)·Exp[i·π·λ·(f3f4f4f3)(fx2+fy2)]iλ·m4(f3f4f4f3)·eiπ·λ·(z1+z2)L2Exp[i·π·λ·(f3f4f4f3){(fx1L)2+fy2}]iλ·m4(f3f4f4f3)·eiπ·λ·(z1+z2)L2Exp[i·π·λ·(f3f4f4f3){(fx+1L)2+fy2}]}.
fbG2=12Exp[i·πλ(x2+y2)(1f31f4)]·Exp[i2πλ(z1+z2)][1+m·eiπ·λ·(z1+z2)L2·Cos(2π·xL)]y.
IbG2=14[1+2·m·Cos(π·λ·(z1+z2)L2)·Cos(2πxL)+m2·Cos2(2πxL)].
IbG2=14[1+m·Cos(2πxL)]2,
z1+z2=2·n·L2λ.
moiréimage={1+Cos(2π·f1·x)}·{1+Cos(2π·f2·x)}=1+Cos(2π·f1·x)+Cos(2π·f2·x)+12Cos[2π·(f1f2)·x]+12Cos[2π·(f1+f2)·x].
[y0α0]=[101f41][1d01][101f31][yiαi].
αo=±n·αi,f3=n·f4,d=f3+f4,
ncon=2·μ·z·Tan[|±αi|]L+2·z·Tan[±αi],
nTLS=2·μ·z·Tan[|±2αi|]L+2·z·Tan[±2αi],
nmodified-TLS=4μ·(zf3f4)·Tan[|±2αi|]L/2+2·(zf3f4)·Tan[±2αi],
αi=δf2±δ,

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