Abstract

We comment on the recent Letter by Chen and Quan [Opt. Lett. 30, 2101 (2005) ] in which a least-squares approach was proposed to cope with the nonparallel illumination in fringe projection profilometry. It is noted that the previous mathematical derivations of the fringe pitch and carrier phase functions on the reference plane were incorrect. In addition, we suggest that the variation of carrier phase along the vertical direction should be considered.

© 2006 Optical Society of America

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  1. L. Chen and C. Quan, Opt. Lett. 30, 2101 (2005).
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2005 (1)

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Equations (8)

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P ( x ) = P E F cos ( α θ ) cos θ .
P ( x ) = P A B ( l 2 + x sin α ) 2 ( l 1 h ) .
ϕ r ( x ) = ϕ 0 + 0 x 2 π P ( u ) d u = ϕ 0 + 0 x 2 π l 1 h P A B ( l 2 + u sin α ) 2 d u = ϕ 0 + 2 π l 1 h P A B l 2 sin α ( 1 l 2 sin α l 2 sin α + x ) = B A + x + C .
A = [ ϕ r ( x 1 ) x 1 ϕ r ( x 2 ) x 2 ] ( x 2 x 3 ) [ ϕ r ( x 2 ) x 2 ϕ r ( x 3 ) x 3 ] ( x 1 x 2 ) [ ϕ r ( x 2 ) ϕ r ( x 1 ) ] ( x 2 x 3 ) [ ϕ r ( x 3 ) ϕ r ( x 2 ) ] ( x 1 x 2 ) ,
C = [ ϕ r ( x 1 ) x 1 ϕ r ( x 2 ) x 2 ] [ ϕ r ( x 3 ) ϕ r ( x 2 ) ] [ ϕ r ( x 2 ) x 2 ϕ r ( x 3 ) x 3 ] [ ϕ r ( x 2 ) ϕ r ( x 1 ) ] [ ϕ r ( x 3 ) ϕ r ( x 2 ) ] ( x 1 x 2 ) [ ϕ r ( x 2 ) ϕ r ( x 1 ) ] ( x 2 x 3 ) ,
B = ( ϕ r ( x 1 ) C ) ( A + x 1 ) ,
ϕ r ( x ) = B A + x + D y + C .
ϕ r ( x ) = a 2 x 2 + a 1 x + b 1 y + c .

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