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  1. Retro-directive is a more appropriate term than autocollimating, which has been widely used in this connection, particularly in the patent literature. Autocollimating has an accepted meaning which is quite different from the present one [see, e.g., R. A. Houstoun, A Treatise on Light (Longmans, Green and Company, 1930), p. 106]. The writer coined the term retro-directive reflector to fill the need for an accurately descriptive term, and used it in testimony in a patent suit before the Federal District Court in Dallas, Texas, during February, 1936. The trade term reflex reflector is perhaps satisfactory as such, but is not sufficiently descriptive for our purposes.
  2. A critical discussion of the applicability of this concept to such a situation will be given in Part II of this series of papers.
  3. R. Kingslake, J. Opt. Soc. Am. 28, 323 (1938).
    [Crossref]
  4. S. A. E. Handbook (Society of Automotive Engineers, 29 West 39th Street, New York, 1939), p. 611.
  5. “I. Fundamental Optical Properties,” to be referred to as Part I.
  6. See also Section B.
  7. The dimension which is significant in determining what distances are “sufficiently great” in a case involving a given divergence limit is the aperture diameter of the reflector. In the case of a mosaic-type triple reflector or a lens-mirror plaque, this dimension will be that of a single sub-unit, since the different sub-units function quite independently of each other.
  8. In all cases where it is necessary that an angular value be expressed in degrees, the symbol will be accented. Where unaccented symbols for angular quantities appear, any units may be used unless a particular unit is explicitly mentioned.
  9. There is no theoretical reason for preferring this particular shape over any other which satisfies the general requirements, but this one is mathematically convenient. Fig. I-7 (Part I) illustrates the assumed shape, both to a uniform and to a logarithmic vertical scale. The curves shown by full lines in that figure correspond to D′=1.5° and those shown by broken lines to D′=2°; the relative peak values (I0) are adjusted in accordance with Eq. (2). The corresponding mathematical expression is given in Section 2 of the mathematical appendix which follows.
  10. Throughout this Appendix, D and δ (unaccented) will represent divergence limit and divergence angle in radians. Of course, where their ratio, δ/D occurs, it is immaterial what unit is used, so long as the same unit is used for both.
  11. “I. Fundamental Optical Properties;” “II. General Basis for Optical Descriptions, Specifications, and Tests;” to be referred to as Parts I and II.
  12. A term proposed in Part I, Section A, as being properly descriptive of the kind of reflectors indicated in the general title of these papers.
  13. See Part II, Section B.
  14. S. A. E. Handbook (Society of Automotive Engineers, New York, 1939), p. 611. Retro-directive reflectors are known to the trade as “reflex reflectors.”
  15. In the language of optics: the lens forms in its principal focal plane a real image of the virtual object at infinity.
  16. R. Kingslake, J. Opt. Soc. Am. 28, 323 (1938). Exactly the same idea was proposed for use in short range photometric measurements on lighthouse beams by A. Blondel in a sealed note deposited with the French Academy of Sciences in 1920 and published in 1929; see A. Blondel, Comptes rendus 188, 1464 (1929), or Sci. Abs., Abstract No. 3543 (1929). The use of this idea in testing automobile head lamps is described by A. Marsat and P. Cibis, Soc. Franc. Elect., Bull. 8, 869 (1938); this paper is covered by Sci. Abs., Abstract No. 4922 (1938).
    [Crossref]
  17. See A. C. Hardy and F. H. Perrin, Principles of Optics (McGraw-Hill, 1932), p. 409.
  18. We here consider the curve as if plotted to uniform scales, not to a logarithmic scale for specific intensity, as recommended in Part I.
  19. This requirement seems to have originated in connection with an early test method (see Harry E. Neal, “Specifications and tests for reflector buttons,” American Highways, pp. 12, 13, July, 1936) which can hardly be said to measure specific intensities. The same percentages were carried over in one state to apply to specific intensity measurements, although in some respects they do not have the same significance when referred to the different test methods. This point will be discussed in detail in Part IV.
  20. This conclusion is in general accord with the usual statistical rule that differences more than four times as great as the probable error of the measurements may be considered as significant, and with the fact that the Electrical Testing Laboratories append to their specific intensity data the remark: “The order of accuracy of the candlepower data in this report is approximately 5 percent.”
  21. For a survey of visual telephotometry, see L. J. Collier, Trans. Illum. Eng. Soc. (London),  3, 141 (1938).
  22. Described in mimeographed material entitled, “Methods of testing reflector buttons, adopted February 18, 1938.”
  23. The eye should not be completely adapted to darkness, nor should one stare at the two sources for more than two or three seconds. It is well to have the meters, notebook, etc., fairly well illuminated, and to glance only briefly at the pair of sources, using several glances to find the setting of the calibrated standard which gives the match.
  24. The candlepower output of the standard is varied by changing the current through its incandescent lamp, and under such conditions the stability of its calibration is not as trustworthy as if a constant current were used.
  25. See A. C. Hardy and F. H. Perrin (reference 7), p. 274; Collier (reference 11); or J. W. T. Walsh, Photometry (Constable, London, 1926), p. 109.
  26. By Lee. Showen, in thesis research for the degree of Master of Science in Engineering Physics at the University of Oklahoma.
  27. This possibility also exists for direct visual matching if the half-silvered mirror is used without the shutter, the adjustment being such that the two images appear side by side. The arrangement would then duplicate the essentials of the artificial-star method of stellar photometry.
  28. For descriptions of artificial stars, see J. W. T. Walsh (reference 15), p. 424; or L. J. Collier (reference 11).

1938 (3)

1936 (1)

This requirement seems to have originated in connection with an early test method (see Harry E. Neal, “Specifications and tests for reflector buttons,” American Highways, pp. 12, 13, July, 1936) which can hardly be said to measure specific intensities. The same percentages were carried over in one state to apply to specific intensity measurements, although in some respects they do not have the same significance when referred to the different test methods. This point will be discussed in detail in Part IV.

Collier, L. J.

For a survey of visual telephotometry, see L. J. Collier, Trans. Illum. Eng. Soc. (London),  3, 141 (1938).

Hardy, A. C.

See A. C. Hardy and F. H. Perrin (reference 7), p. 274; Collier (reference 11); or J. W. T. Walsh, Photometry (Constable, London, 1926), p. 109.

See A. C. Hardy and F. H. Perrin, Principles of Optics (McGraw-Hill, 1932), p. 409.

Houstoun, R. A.

Retro-directive is a more appropriate term than autocollimating, which has been widely used in this connection, particularly in the patent literature. Autocollimating has an accepted meaning which is quite different from the present one [see, e.g., R. A. Houstoun, A Treatise on Light (Longmans, Green and Company, 1930), p. 106]. The writer coined the term retro-directive reflector to fill the need for an accurately descriptive term, and used it in testimony in a patent suit before the Federal District Court in Dallas, Texas, during February, 1936. The trade term reflex reflector is perhaps satisfactory as such, but is not sufficiently descriptive for our purposes.

Kingslake, R.

Neal, Harry E.

This requirement seems to have originated in connection with an early test method (see Harry E. Neal, “Specifications and tests for reflector buttons,” American Highways, pp. 12, 13, July, 1936) which can hardly be said to measure specific intensities. The same percentages were carried over in one state to apply to specific intensity measurements, although in some respects they do not have the same significance when referred to the different test methods. This point will be discussed in detail in Part IV.

Perrin, F. H.

See A. C. Hardy and F. H. Perrin, Principles of Optics (McGraw-Hill, 1932), p. 409.

See A. C. Hardy and F. H. Perrin (reference 7), p. 274; Collier (reference 11); or J. W. T. Walsh, Photometry (Constable, London, 1926), p. 109.

Showen, Lee.

By Lee. Showen, in thesis research for the degree of Master of Science in Engineering Physics at the University of Oklahoma.

Walsh, J. W. T.

For descriptions of artificial stars, see J. W. T. Walsh (reference 15), p. 424; or L. J. Collier (reference 11).

American Highways (1)

This requirement seems to have originated in connection with an early test method (see Harry E. Neal, “Specifications and tests for reflector buttons,” American Highways, pp. 12, 13, July, 1936) which can hardly be said to measure specific intensities. The same percentages were carried over in one state to apply to specific intensity measurements, although in some respects they do not have the same significance when referred to the different test methods. This point will be discussed in detail in Part IV.

J. Opt. Soc. Am. (2)

Trans. Illum. Eng. Soc. (London) (1)

For a survey of visual telephotometry, see L. J. Collier, Trans. Illum. Eng. Soc. (London),  3, 141 (1938).

Other (24)

Described in mimeographed material entitled, “Methods of testing reflector buttons, adopted February 18, 1938.”

The eye should not be completely adapted to darkness, nor should one stare at the two sources for more than two or three seconds. It is well to have the meters, notebook, etc., fairly well illuminated, and to glance only briefly at the pair of sources, using several glances to find the setting of the calibrated standard which gives the match.

The candlepower output of the standard is varied by changing the current through its incandescent lamp, and under such conditions the stability of its calibration is not as trustworthy as if a constant current were used.

See A. C. Hardy and F. H. Perrin (reference 7), p. 274; Collier (reference 11); or J. W. T. Walsh, Photometry (Constable, London, 1926), p. 109.

By Lee. Showen, in thesis research for the degree of Master of Science in Engineering Physics at the University of Oklahoma.

This possibility also exists for direct visual matching if the half-silvered mirror is used without the shutter, the adjustment being such that the two images appear side by side. The arrangement would then duplicate the essentials of the artificial-star method of stellar photometry.

For descriptions of artificial stars, see J. W. T. Walsh (reference 15), p. 424; or L. J. Collier (reference 11).

S. A. E. Handbook (Society of Automotive Engineers, 29 West 39th Street, New York, 1939), p. 611.

“I. Fundamental Optical Properties,” to be referred to as Part I.

See also Section B.

The dimension which is significant in determining what distances are “sufficiently great” in a case involving a given divergence limit is the aperture diameter of the reflector. In the case of a mosaic-type triple reflector or a lens-mirror plaque, this dimension will be that of a single sub-unit, since the different sub-units function quite independently of each other.

In all cases where it is necessary that an angular value be expressed in degrees, the symbol will be accented. Where unaccented symbols for angular quantities appear, any units may be used unless a particular unit is explicitly mentioned.

There is no theoretical reason for preferring this particular shape over any other which satisfies the general requirements, but this one is mathematically convenient. Fig. I-7 (Part I) illustrates the assumed shape, both to a uniform and to a logarithmic vertical scale. The curves shown by full lines in that figure correspond to D′=1.5° and those shown by broken lines to D′=2°; the relative peak values (I0) are adjusted in accordance with Eq. (2). The corresponding mathematical expression is given in Section 2 of the mathematical appendix which follows.

Throughout this Appendix, D and δ (unaccented) will represent divergence limit and divergence angle in radians. Of course, where their ratio, δ/D occurs, it is immaterial what unit is used, so long as the same unit is used for both.

“I. Fundamental Optical Properties;” “II. General Basis for Optical Descriptions, Specifications, and Tests;” to be referred to as Parts I and II.

A term proposed in Part I, Section A, as being properly descriptive of the kind of reflectors indicated in the general title of these papers.

See Part II, Section B.

S. A. E. Handbook (Society of Automotive Engineers, New York, 1939), p. 611. Retro-directive reflectors are known to the trade as “reflex reflectors.”

In the language of optics: the lens forms in its principal focal plane a real image of the virtual object at infinity.

See A. C. Hardy and F. H. Perrin, Principles of Optics (McGraw-Hill, 1932), p. 409.

We here consider the curve as if plotted to uniform scales, not to a logarithmic scale for specific intensity, as recommended in Part I.

Retro-directive is a more appropriate term than autocollimating, which has been widely used in this connection, particularly in the patent literature. Autocollimating has an accepted meaning which is quite different from the present one [see, e.g., R. A. Houstoun, A Treatise on Light (Longmans, Green and Company, 1930), p. 106]. The writer coined the term retro-directive reflector to fill the need for an accurately descriptive term, and used it in testimony in a patent suit before the Federal District Court in Dallas, Texas, during February, 1936. The trade term reflex reflector is perhaps satisfactory as such, but is not sufficiently descriptive for our purposes.

A critical discussion of the applicability of this concept to such a situation will be given in Part II of this series of papers.

This conclusion is in general accord with the usual statistical rule that differences more than four times as great as the probable error of the measurements may be considered as significant, and with the fact that the Electrical Testing Laboratories append to their specific intensity data the remark: “The order of accuracy of the candlepower data in this report is approximately 5 percent.”

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Figures (12)

Fig. I-1
Fig. I-1

Return beams from sign reflectors.

Fig. I-2
Fig. I-2

Signal strength depends on spread given return beam.

Fig. I-3
Fig. I-3

Contrasting types of reflection. (a) Ordinary reflection; (b) retro-directive reflection.

Fig. I-4
Fig. I-4

Triple reflectors. (a) Three perpendicular mirrors; (b) mosaic-type triple reflector.

Fig. I-5
Fig. I-5

Lens-mirror button and plaque. (a) Essential parts of lens-mirror button; (b) lens-mirror plaque.

Fig. I-6
Fig. I-6

Entrance and divergence angles.

Fig. I-7
Fig. I-7

Divergence-angle characteristics. (a) Uniform vertical scale; (b) logarithmic vertical scale.

Fig. II-1
Fig. II-1

Entrance, divergence, and azimuth angles.

Fig. II-2
Fig. II-2

Orientation angle, β. γ1, γ2 measured from normal position shown.

Fig. III-1
Fig. III-1

Use of lens at short test distance.

Fig. III-2
Fig. III-2

Illuminating cone and divergence angle.

Fig. III-3
Fig. III-3

Optical-substitution telephotometer.

Equations (15)

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sin γ 2 = - sin α sin γ ,
cos γ 1 = cos γ / ( 1 - sin 2 α sin 2 γ ) 1 2 .
I = 7.3 k A / D 2 ,
I 0 = 33.4 k A / D 2 ,
C = ( 360 ) 2 k E A 4 × 144 π 3 D 2 = 7.3 k E A D 2 ,
I = C / E = 7.3 k A / D 2 .
I = I 0 e - 4.6 δ 2 / D 2 .
2 π E 0 I ( δ ) δ d δ .
k E A / 144 = 2 π E I 0 0 e - 4.6 δ 2 / D 2 δ d δ = π E I 0 D 2 / 4.6.
I 0 = 33.4 k A / D 2 ,
I = 33.4 k A D 2 e - 4.6 δ 2 / D 2 .
I = I 0 f ( δ / D ) ,
0 f ( δ / D ) δ d δ = D 2 0 f ( x ) x d x ,
I 0 = p k A / D 2 ,
E = π B sin 2 θ ,