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Timestamp: 2016-09-26 19:07:07
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Patent US6400391 - Optical scanning lens, optical scanning device and image forming apparatus - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsAn optical scanning lens is used in a scanning and image forming optical system which gathers a light flux deflected by a light deflector in the vicinity of a surface to be scanned. The lens is formed by plastic molding of polyolefin resin, and the following condition is satisfied: 0<|Δn(x)−min[Δn(x)]|<34�10−5,...http://www.google.com/patents/US6400391?utm_source=gb-gplus-sharePatent US6400391 - Optical scanning lens, optical scanning device and image forming apparatusAdvanced Patent SearchTry the new Google Patents, with machine-classified Google Scholar results, and Japanese and South Korean patents.Publication numberUS6400391 B1Publication typeGrantApplication numberUS 09/588,342Publication dateJun 4, 2002Filing dateJun 6, 2000Priority dateJun 9, 1999Fee statusPaidAlso published asUS6744545, US6870652, US7072127, US20020163571, US20040196520, US20050128615Publication number09588342, 588342, US 6400391 B1, US 6400391B1, US-B1-6400391, US6400391 B1, US6400391B1InventorsHiroyuki Suhara, Satoru Itoh, Tatsuya Ito, Takeshi Ueda, Yoshinori Hayashi, Magane Aoki, Kenichi Takanashi, Takao Yamaguchi, Taira Kouchiwa, Koji Hirakura, Seizo SuzukiOriginal AssigneeRicoh Company, Ltd.Export CitationBiBTeX, EndNote, RefManPatent Citations (21), Non-Patent Citations (6), Referenced by (128), Classifications (18), Legal Events (4) External Links: USPTO, USPTO Assignment, EspacenetOptical scanning lens, optical scanning device and image forming apparatus
US 6400391 B1Abstract
0<|Δn(x)−min[Δn(x)]|<34�10−5 (A)
where Δn(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[Δn(x)] denotes the minimum value of the Δn(x).
0<|Δn|<8.5�10−5 (B)
where, when Δn(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately �1 mm from a center of the light flux, in a range which the light flux passes through, in the lens, Δn denotes a coefficient of second order in ‘second-order least-square approximation’ of the Δn(x).
where Δn(x) denotes a refractive-index distribution existing inside the lens, in a range which the light flux passes through, in the lens, and min[Δn(x)] denotes the minimum value of the Δn(x), and, also, the following condition is satisfied
where, when Δn(x) denotes a refractive-index distribution existing inside the lens, in a range between approximately �1 mm from a center of the light flux, in a range which the light flux passes through, in the lens, Δn denotes a coefficient of second order in second-order least-square approximation of the Δn(x).
0.4�10−5 <|Δn(x)−min[Δn(x)]|<16�10−5 (C)
0.1�10−5 <|Δn|<4.0�10−5 (D)
‘A range, which a light flux passes through, of a lens’, is ‘a range, which a light flux deflected by a light deflector passes through when being deflected, of an optical scanning lens’. In details, with respect to main scanning direction, ‘a range, which a light flux passes through and which corresponds to an effective writing width of a surface to be scanned, of a lens’, is a range, which a deflected light flux passes through, in the lens. With respect to sub-scanning directions, it is preferable that ‘a range, which a light flux passes through and which corresponds to an effective writing width of a surface to be scanned, of a lens’, is a range, which a deflected light flux passes through, in the lens. With respect to sub-scanning directions, it is preferable that ‘a range, which a light flux passes through, of a lens’, is ‘one on the order of between �2 mm in consideration of change in an angle at which a light flux emitted from a light source and/or surface inclination of a light deflector’.
[∫n(x, y)dy]/d(x)
where d(x) denotes a thickness of the lens in the optical-axis directions with respect to the x direction. The integration is performed through the thickness of the lens d(x).
The cell 21 filled with the object to be examined A and test liquid B is an object, a refractive index of which is uniform through the entirety thereof, and can incident surface and an emitting surface of which are parallel to one another. Accordingly, the wave to be examined ‘b’ transmitted by the cell 21 is emitted therefrom as being an approximately parallel light flux. When a refractive-index distribution inside the object to be examined A is non-uniform, a wave surface of the wave to be examined ‘b’ emitted from the cell 21 has ‘a curved-surface shape depending on the refractive-index distribution’. Interference fringes, an image of which is formed on the image pickup surface of the interference-fringe detector 15, develop due to interference between the wave to be examined ‘b’ of the above-mentioned curved-surface shape and the reference wave ‘a’ which is a plane wave. The curved-surface shape of the wave to be examined ‘b’ can be measured by well-known analysis of interference fringes.
Δn(x)={WF(x)−WF(0)}�λ/d(x)
Thus, a refractive-index distribution Δn(x) can be calculated for an arbitrary measurement section. A refractive-index distribution in main scanning directions is such that variation is small in comparison to that in sub-scanning directions. Therefore, by measuring for several specific sections (of middle portion, peripheral portion and so forth), it is possible to grasp a refractive-index distribution of the entirety of an optical scanning lens. It is possible to use a refractive-index distribution measured for one section of a middle portion or the like as a representative one of an overall refractive-index distribution, for those such as mass-produced ones for which mold conditions are stable. A change of a measurement section can be performed by changing a position relationship between the linear CCD and a lens to be examined to be that such that the lens to be examined is moved in z directions relative to the linear CCD.
In the above-described method, Δn(x) is calculated from ‘an optical-axis directional thickness directionally added-up transmitted wave surface’. Accordingly, although ‘a refractive-index distribution in optical-axis directions’ such as that shown in FIG. 2D cannot be obtained, average data Δn(x) obtained as a result of it being added up in optical-axis directions is sufficient to grasp optical characteristics of an optical scanning lens. Further, because Δn(x) is of one dimension, this can be easily managed as an evaluation item advantageously.
Δn(x)≈n0+n1�x+n2�x 2 + . . . +nm�x m (1)
(The symbol ‘≈’ signifies ‘is approximately equal to’.)
Then, by obtaining respective coefficients n0, n1, n2, . . . , nm (coefficient of a term of a highest mth order), it is possible to obtain a refractive-index distribution at a position of a coordinate ‘x’ on an x-axis directly. Although the number of order of the above-mentioned polynominal is arbitrary, the second order is selected, for example, and the following equation is used.
Δn(x)=n 0 +n1�x+Δn�x 2+δ(x) (2)
In the right side of this equation, ‘a coefficient of second order Δn’ affects optical characteristics largely. Because a coefficient of first order n0 has a small optical influence, it is possible to neglect the coefficient. δ(x) is a residual due to second-order approximation and is a slight amount. Accordingly, the following expression can be obtained.
Δn(x)≈n 0 +Δn�x 2 (3)
In the above expression (3), Δn is determined by a least squares method.
In the above expression (3), the coefficient of second order Δn functions as ‘a lens power’. Because a diameter of a light flux passing through an optical scanning lens is on the order of 1 mm in general, a range of ‘x’ when Δn is calculated is determined to be one between �1 mm, here.
As described above, a refractive-index distribution can be regarded as ‘functioning as a lens’. Therefore, when considering ‘a lens equivalent to a refractive-index distribution’, it is possible to express a relationship between a focal length f′ of the equivalent lens, Δn, and a lens thickness t, by the following expression.
f′≈1/(2�Δn�t) (4)
(When an optical scanning lens is a compound lens consisting of a plurality of single lenses, a lens thickness t in the above expression (4) is ‘the sum in thickness of respective single lenses of the optical scanning lens’.)
Δf≈f 2 /f′ (5)
A shift in position of image formation ΔS′ due to a refractive-index distribution can be expressed using the following thin lens's paraxial image-formation formula:
(1/S′=1/S+1/f)
ΔS′≈{S/(S+f)}2 �Δf ={f�S/(S+f)}2 /f′ =(S′)2�(2�Δn�t) (6)
When L denotes a distance between a deflection reflecting surface of a light deflector and a surface to be scanned as shown in FIG. 1 and β denotes a lateral magnification of an optical scanning lens 30, the above expression (6) can be expressed by approximation as follows.
ΔS′≈{β/(β−1)�L} 2�(2�Δn�t) (7)
By using the above expression (7), an amount of defocus ΔS′ can be obtained from the above-mentioned ‘Δn’ of an optical scanning lens by calculation.
w≈1.487�d 2/λ (8)
When it is possible to control a shift in position of image formation ΔS′ in the range of this allowance of focal depth w, it is possible to obtain a stable beam-spot diameter on a surface to be scanned. That is, an optical scanning lens should be made as a lens which satisfies the following condition.
w≧ΔS′ (9)
By using the above-expression (9), it is possible to determine ‘a magnitude of Δn’ so that a beam-spot diameter can be controlled in an allowable range. Because a refractive-index distribution is determined depending on a degree of a magnitude of Δn, it is possible to achieve a satisfactory beam-spot diameter by controlling a refractive-index distribution Δn(x) within a predetermined range.
When a refractive-index distribution Δn(x) denotes non-uniformity of refractive index existing inside the lens in the range between �2 mm in sub-scanning directions and min[Δn(x)] denotes the minimum value thereof, it can be determined that these should satisfy
as a result of values such that Δn=8.5�10−5 and x=2 being substituted for Δn and x in the following expression
so that ‘a shift in lens shape’ be within an allowance. When |Δn(x)−min[Δn(x)]|≧34�10−5, optical characteristics deteriorate regardless of shape and size of a lens.
0.1�10−5 <|Δn|<4.0�10−5 (D) 0.4�10−5 <|Δn(x)−min[Δn(x)]|<16�10−5 (C)
When |Δn| exceeds the upper limit 4.0�10−5 and increases, it is necessary to limit a wavelength λ to be used and/or decreases an optical magnification |β|, and restrictions on an optical design become strict. On the other hand, when |Δn| exceeds the lower limit 0.1�10−5 and decreases, not only a measurement error cannot be ignored, but also a cooling time required for molding increases, manufacturing efficiency deteriorates, and cost increases.
Results of measurements of refractive-index distributions Δn(x) for these samples are shown in FIGS. 6 through 10. In each of FIGS. 6 through 10, a refractive-index distribution Δn(x) of a vertical axis is indicated assuming that a reference value of Δn(x) is 0, ‘short-length direction’ indicated for a horizontal axis is sub-scanning directions, and, is the above-mentioned x direction, and the range between �2 nm of upper and lower limits of the horizontal axis is ‘a range in the sub-scanning directions which a light flux passes through’. FIGS. 7 and 9 show three types of refractive-index distributions Δn(x) for different ‘lens heights’, respectively. A ‘height’ in the figures indicates a position of plane in main scanning directions, in which plane measurement of Δn(x) is made, assuming that the optical-axis position is 0. That is, in FIGS. 7 and 9, the three types of refractive-index distributions Δn(x) are refractive-index distributions in respective positions in the main scanning directions such that z=0, 25, and 50 (mm) assuming that the optical-axis position is such that z=0.
|Δn(x)−min[Δn(x)]|≦53.9�10−5, Δn=10.3�10−5 [1/mm2]
|Δn(x)−min[Δn(x)]|≦2.1�10−5, Δn=0.5�10−5 [1/mm2]
|Δn(x)−min[Δn(x)]|≦29.7�10−5, Δn=8.3�10−5 [1/mm2]
|Δn(x)−min[Δn(x)]|≦13.8�10−5, Δn=3.8�10−5 [1/mm2]
|Δn(x)−min[Δn(x)]|≦0.47�10−5, Δn=−0.2�10−5 [1/mm2]
As described above, the optical scanning lens 30 is designed to an optimum one in the conditions such that the length of light path L=200 (mm), the lateral magnification β=−1.0, and the lens thickness t=10 (mm). An amount of defocus developing due to a refractive-index distribution inside the lens is obtained by the expression (4) as follows: 20.6 mm for the sample S1, 1.0 mm for the sample S2, 16.6 mm for the sample S3, 7.6 mm for the sample S4 and −0.4 mm for the sample S5. When these are compared with the above-described allowance of focal depth w (w=18.2 (mm) when a target beam-spot diameter d=70 (μm) and a wave length of the semiconductor laser λ=400 (nm); w=18.5 (mm) when a target beam-spot diameter d=90 (μm) and a wave length of the semiconductor laser λ=650 (nm)), for the sample S1, because the amount of defocus is larger than the allowance of focal depth, the sample S1 is rejected as an optical scanning lens. However, for each of the samples S2 through S5, because the amount of defocus is controlled within the allowance of focal depth, these samples can be used as optical scanning lenses. It is noted that results of actually measuring allowances of focal depth by measuring beam diameters were similar to the above calculation results, and, thereby, correctness of the calculation results was proved.
However, these conditions (C) and (D) are not limited for the above-mentioned optical systems {circle around (1)} through {circle around (4)}.
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SATORU;ITO, TATSUYA;AND OTHERS;REEL/FRAME:011184/0175;SIGNING DATES FROM 20000711 TO 20000714Nov 14, 2005FPAYFee paymentYear of fee payment: 4Nov 4, 2009FPAYFee paymentYear of fee payment: 8Dec 2, 2013FPAYFee paymentYear of fee payment: 12RotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services