Far field of gratings with rough strips

Sanchez‐Brea, Luis Miguel; Torcal-Milla, Francisco José; Bernabéu, Eusebio

doi:10.1364/josaa.25.000828

Cited by 21 publications

(12 citation statements)

References 12 publications

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“…The second amplitude grating, G 2 ͑x͒ =1−G 1 ͑x͒, is formed by strips with two constant levels, in the same way as G 1 ͑x͒. The sum of these two amplitude gratings [13],…”

Section: Theoretical Approachmentioning

confidence: 99%

“…Examples of gratings with roughness are steel tape gratings used in displacement measurement systems [12]. In a previous paper we analyzed the far-field diffraction pattern of transmission gratings whose strips present two different roughness levels, one of them smooth and the other one rough [13]. The efficiency of the diffraction orders was shown to depend on the statistical properties of the roughness.…”

Section: Introductionmentioning

confidence: 99%

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Self-imaging of gratings with rough strips

2008

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We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low-and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work

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“…The second amplitude grating, G 2 ͑x͒ =1−G 1 ͑x͒, is formed by strips with two constant levels, in the same way as G 1 ͑x͒. The sum of these two amplitude gratings [13],…”

Section: Theoretical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Self-imaging of gratings with rough strips

2008

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“…Also, stochastical irregularities in the shape of the edges can be produced. This effect is not normally present in chrome on glass gratings or phase glass gratings, but strips with rough edges can be detected in some other manufacturing processes, such as laser ablation or chemical attack [13,18].…”

Section: /mentioning

confidence: 97%

“…Amplitude or phase gratings are used in most applications. Also, other kind of gratings is possible, such as polarization gratings [8][9][10] or gratings with random microscopic irregularities in the topography [11][12][13]. In the far field the beam is divided into diffraction orders whose directions are given by the well-known grating equation [1].…”

Section: Introductionmentioning

confidence: 99%

Diffraction of gratings with rough edges

Torcal-Milla¹,

Sanchez‐Brea²,

Bernabéu³

2008

Opt. Express

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Abstract:We analyze the far field and near field diffraction pattern produced by an amplitude grating whose strips present rough edges. Due to the stochastic nature of the edges a statistical approach is performed. The grating with rough edges is not purely periodic, although it still divides the incident beam in diffracted orders. The intensity of each diffraction order is modified by the statistical properties of the irregular edges and it strongly decreases when roughness increases except for the zero-th diffraction order. This decreasing firstly affects to the higher orders. Then, it is possible to obtain an amplitude binary grating with only diffraction orders -1, 0 and +1. On the other hand, numerical simulations based on Rayleigh-Sommerfeld approach have been used for the case of near field. They show that the edges of the self-images are smoother than the edges of the grating. Finally, we fabricate gratings with rough edges and an experimental verification of the results is performed. Opt. Soc. Am. A 11, 1874-1885 (1994

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“…For ideal gratings, the orders characteristics are obtained from the Fourier decomposition [4][5][6][7][8][9][10]. Nevertheless real gratings are not purely periodic, since they are affected by flaws due to different fabrication processes [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Far field of binary phase gratings with errors in the height of the strips

Rico-Garcı́a

Sanchez‐Brea

2009

Modeling Aspects in Optical Metrology II

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Diffraction gratings are not always ideal but, due to the fabrication process, several errors can be produced. In this work we show that when the strips of a binary phase diffraction grating present certain randomness in their height, the intensity of the diffraction orders varies with respect to that obtained with a perfect grating. To show this, we perform an analysis of the mutual coherence function and then, the intensity distribution at the far field is obtained. In addition to the far field diffraction orders, a "halo" that surrounds the diffraction order is found, which is due to the randomness of the strips height.

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Far field of gratings with rough strips

Cited by 21 publications

References 12 publications

Self-imaging of gratings with rough strips

Self-imaging of gratings with rough strips

Diffraction of gratings with rough edges

Far field of binary phase gratings with errors in the height of the strips

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