Abstract

A filtering macrolens was developed to simultaneously achieve macro-optical imaging and correct spectrum aberration. The macrolens was a doublet lens comprising a filtering lens and a close-up lens. The shape of the filtering lens was designed to eliminate the optical path differences between the light rays in the absorbing medium. The close-up lens was designed to decrease the effective focal length of an ordinary camera lens to provide high magnification capability and collimate the diverging beams through the filtering lens. Experimental results demonstrated that the spectrum uniformity of the macro-optical images was markedly improved by the filtering macrolens. This innovation may be used in finite conjugate optical systems.

© 2013 Optical Society of America

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References

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  1. S. S. Zumdahl, Chemical Principles, 5th ed. (Houghton, 2003), pp. A18–A20.
  2. D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis, 6th ed. (Brooks/Cole, 2007), pp. 336–342.
  3. R. B. Tagirow and L. P. Tagirov, “Lambert formula—Bouguer absorption law?” Russ. Phys. J. 40, 664–669 (1997).
    [CrossRef]
  4. Wikipedia, “Beer-Lambert law,” http://en.wikipedia.org/wiki/Beer-Lambert_law .
  5. Wikipedia, “Mathematical descriptions of opacity,” http://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity#cite_ref-Griffiths9.4.3_2-1 .
  6. Alex Ryer, Light Measurement Handbook (International Light, 1998), p. 14.
  7. Steven K. Dew and Robert R. Parsons, “Absorbing filter to flatten Gaussian beams,” Appl. Opt. 31, 3416–3419 (1992).
    [CrossRef]
  8. S. O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice-Hall, 2001), pp. 16–22.
  9. H. Abitan, H. Bohr, and P. Buchhave, “Correction to the Beer–Lambert–Bouguer law for optical absorption,” Appl. Opt. 47, 5354–5357 (2008).
    [CrossRef]
  10. Wikipedia, “Macro photography,” http://en.wikipedia.org/wiki/Macro_photography .
  11. Schott, “Longpass filters,” http://www.schott.com/advanced_optics/english/products/filteroverviewdetail-longpass.html .
  12. Wikipedia, “Close-up filter,” http://en.wikipedia.org/wiki/Close-up_filter .
  13. H. Eugene, Optics (Addison-Wesley, 1998), pp. 111–120.

2008 (1)

1997 (1)

R. B. Tagirow and L. P. Tagirov, “Lambert formula—Bouguer absorption law?” Russ. Phys. J. 40, 664–669 (1997).
[CrossRef]

1992 (1)

Abitan, H.

Bohr, H.

Buchhave, P.

Crouch, S. R.

D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis, 6th ed. (Brooks/Cole, 2007), pp. 336–342.

Dew, Steven K.

Eugene, H.

H. Eugene, Optics (Addison-Wesley, 1998), pp. 111–120.

Holler, F. J.

D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis, 6th ed. (Brooks/Cole, 2007), pp. 336–342.

Kasap, S. O.

S. O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice-Hall, 2001), pp. 16–22.

Parsons, Robert R.

Ryer, Alex

Alex Ryer, Light Measurement Handbook (International Light, 1998), p. 14.

Skoog, D. A.

D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis, 6th ed. (Brooks/Cole, 2007), pp. 336–342.

Tagirov, L. P.

R. B. Tagirow and L. P. Tagirov, “Lambert formula—Bouguer absorption law?” Russ. Phys. J. 40, 664–669 (1997).
[CrossRef]

Tagirow, R. B.

R. B. Tagirow and L. P. Tagirov, “Lambert formula—Bouguer absorption law?” Russ. Phys. J. 40, 664–669 (1997).
[CrossRef]

Zumdahl, S. S.

S. S. Zumdahl, Chemical Principles, 5th ed. (Houghton, 2003), pp. A18–A20.

Appl. Opt. (2)

Russ. Phys. J. (1)

R. B. Tagirow and L. P. Tagirov, “Lambert formula—Bouguer absorption law?” Russ. Phys. J. 40, 664–669 (1997).
[CrossRef]

Other (10)

Wikipedia, “Beer-Lambert law,” http://en.wikipedia.org/wiki/Beer-Lambert_law .

Wikipedia, “Mathematical descriptions of opacity,” http://en.wikipedia.org/wiki/Mathematical_descriptions_of_opacity#cite_ref-Griffiths9.4.3_2-1 .

Alex Ryer, Light Measurement Handbook (International Light, 1998), p. 14.

Wikipedia, “Macro photography,” http://en.wikipedia.org/wiki/Macro_photography .

Schott, “Longpass filters,” http://www.schott.com/advanced_optics/english/products/filteroverviewdetail-longpass.html .

Wikipedia, “Close-up filter,” http://en.wikipedia.org/wiki/Close-up_filter .

H. Eugene, Optics (Addison-Wesley, 1998), pp. 111–120.

S. O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice-Hall, 2001), pp. 16–22.

S. S. Zumdahl, Chemical Principles, 5th ed. (Houghton, 2003), pp. A18–A20.

D. A. Skoog, F. J. Holler, and S. R. Crouch, Principles of Instrumental Analysis, 6th ed. (Brooks/Cole, 2007), pp. 336–342.

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Figures (9)

Fig. 1.
Fig. 1.

Thickness of a normal absorbing filter is constant (t0). When diverging light beams enter the filter medium, the OPL increases (t2>t1>t0) with increasing divergence angle (θ2>θ1>θ0). According to the Beer–Lambert–Bouguer law, the optical density changes and spectral red-shift occurs. The reflection loss also increases with increasing divergence angle. These effects cause poor uniformity of the spectral transmission.

Fig. 2.
Fig. 2.

Optical model of the meniscus filtering lens. The light ray starts from point C with a divergence angle θ. It enters the lens at point B and leaves at point E. For ideal spectrum aberration correction, the traveling distance of the light in the medium must be equal to the lens center displacement t0.

Fig. 3.
Fig. 3.

Radius of the curvature of the filtering lens versus the divergence angles of the light rays for two lens shapes. For prefect spectrum aberration correction, the filtering lens must be aspherical. However, a spherical filtering lens with a suitable radius of curvature can also obtain favorable spectrum aberration correction.

Fig. 4.
Fig. 4.

Illustration of the distance that the light travels in the medium versus the divergence angles of the light rays for the normal filter (curve 1), the aspherical filtering lens (line 2), and the spherical filtering lenses with various radii of curvatures (curves 3–5).

Fig. 5.
Fig. 5.

External transmission curves of (a) the normal filter and (b) the filtering lens at divergence angles of 0°, 30°, 45°, and 60°. The λc is the cutoff wavelength of the filter and lens material.

Fig. 6.
Fig. 6.

Illustration of the optical simulation for the close-up lens and filtering lenses.

Fig. 7.
Fig. 7.

Overview of the (a) normal filter, filtering lens, and close-up lens and (b) assembly of the camera lens and filtering macrolens (filtering and close-up lenses).

Fig. 8.
Fig. 8.

Experimental setup of the DSLR and the filtering macrolens for the macro-optical imaging. A long pass glass (OG530) was the sample, illuminated by a uniform white light source.

Fig. 9.
Fig. 9.

Optical macro-images captured via (a) the normal filter and (b) the filtering lens. The diagram of (c) the R curves and (d) the G curves related to the diagonal line of the averaged images for the normal filter and filtering lens, respectively. The dotted lines shown in (c) and (d) represent the center of the images.

Equations (11)

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τ(λ)=10α(λ)l,
T1(λ)=P(λ)·τ2(λ)d1d2,
n·sinθt=n0·sinθi,
W=Rc·[1tanθi·(1+tanθ·tanθi)tanθ·(1+tan2θi)·cos(θθi)].
θb=tan1(t0·sin·θθi)Rct0·cos(θθi)).
BD¯=Rc{11cosθb·[1tanθbtanθb+tan(θθi)].
BD¯BE¯·cos(θtθb)=to·cos(θtθb).
Runpolarised=Rs+Rp2,
Rs=|n1·cosθin2·cosθtn1·cosθi+n2·cosθt|2
Rs=|n1·cosθtn2·cosθin1·cosθt+n2·cosθi|2,
P=1R1R2,

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