Optical apparatus, image forming apparatus, and image reading apparatus

An optical apparatus includes: a light source including multiple light-emitting points arrayed in a first direction; and an imaging optical system including multiple lens optical systems arrayed in the first direction. The imaging optical system forms images of the multiple light-emitting points on a light-receiving surface. In a first cross-section and in a second cross-section, half-value of a maximum value of angle of divergence of an imaging optical flux input to the light-receiving surface, resolution, and a size of each image of the plurality of light-emitting points formed on the light-receiving surface, satisfy predetermined conditions.

TECHNICAL FIELD

The present invention relates to an optical apparatus, and more particularly an optical apparatus suitably applied to an image forming apparatus or image reading apparatus, for example.

BACKGROUND ART

As of recent, there have been developed image forming apparatuses and image reading apparatus including optical apparatuses which have a lens array made up of multiple lenses. This configuration enables realization of reduction in apparatus size and costs, in comparison with configurations scanning a photosensitive member by a polygon mirror, configurations reading images using multiple lenses and mirrors, and so forth.

Japanese Patent Application Laid-Open No. 63-274915 (hereinafter referred to as “PTL 1”) discloses a lens array in which multiple lenses are arrayed in one direction (first direction). Each of the multiple lenses perform erecting same-size imaging of an object within a cross-section parallel to the first direction and optical axis direction (first cross-section), and perform inverted same-size imaging of an object within a cross-section perpendicular to the first direction (second cross-section). This configuration enables the lens power to be smaller within the second cross-section, as compared with an optical system performing erecting same-size imaging in the first cross-section. This is advantageous in realizing both resolution and light available efficiency.

Now, let us consider depth of field as being indicative of imaging capabilities of the lens array, in addition to resolution. Depth of field indicates a range on the optical axis over which a predetermined resolution can be obtained in front of and behind the image field position. Normally, a lens array having a great depth of field has lower light available efficiency, and a lens array having great light available efficiency has lower depth of field. Further, a lens array has to have resolution ensured within the first and second cross-sections, so consideration has to be given to common field of depth within both cross-sections.

However, the lens array disclosed in PTL 1 does not take into consideration the common depth of field within both the first and second cross-sections when receiving input of light rays from the light-emission points of an array light source. That is to say, the lens array described in PTL 1 is of a configuration where the depth of field in the first cross-section and the depth of field in the second cross-section are different. The common depth of field is determined by the smaller of the depths of field in both cross-sections, so the lens array according to PTL 1 has secured unnecessarily great depth of field in one cross-section. Accordingly, the lens array disclosed in PTL 1 is not an optimal configuration for realizing both resolution and light available efficiency, since light available efficiency is lost by the amount exceeding the common depth of field at one cross-section.

Also, the common depth of field of the lens array differs according to the position of each light-emitting point of the array light source, as well. Accordingly, difference in light-emitting point has to be taken into consideration to realize both resolution and light available efficiency, but there is no disclosure or suggestion of taking difference in light-emitting point with regard to the lens array described in PTL 1.

CITATION LIST

Patent Literature

SUMMARY OF INVENTION

It has been found desirable to provide an optical apparatus in which both light available efficiency and imaging capabilities are realized at each of the first and second cross-sections.

An optical apparatus according to an aspect of the present invention includes: a light source including a plurality of light-emitting points arrayed in a first direction; and an imaging optical system including a plurality of lens optical systems arrayed in the first direction. The imaging optical system forms images of the plurality of light-emitting points on a light-receiving surface. Conditions of

are satisfied, where

in a first cross-section which is parallel to the first direction and an axial direction of the lens optical systems, θmrepresents a half-value of a maximum value of angle of divergence (aperture angle) of an imaging optical flux input to the light-receiving surface, Pmrepresents resolution, and Dmrepresents a size of each image of the plurality of light-emitting points, formed on the light-receiving surface, and

in a second cross-section which is perpendicular to the first direction, θsrepresents a half-value of a maximum value of angle of divergence (aperture angle) of an imaging optical flux input to the light-receiving surface, Psrepresents resolution, and Dsrepresents a size of each image of the plurality of light-emitting points, formed on the light-receiving surface.

DESCRIPTION OF EMBODIMENTS

Description will be made below regarding embodiments of the present invention, with reference to the drawings.

First Embodiment

FIGS. 1A through 1Care schematic diagrams of principal portions of an optical apparatus according to a first embodiment applied to an image forming apparatus.FIG. 1Aillustrates a first cross-section (X-Y cross-section),FIG. 1Billustrates a second cross-section (Z-X cross-section), andFIG. 1Cis a frontal view from the optical axis direction (X direction). The optical apparatus according to the present embodiment includes a light source101including multiple light-emitting points arrayed on an object plane, and an imaging optical system105which condenses multiple light rays emitted from the light source101upon a light-receiving surface106(image plane).

The light source101includes multiple light-emitting points arrayed at equal intervals in a first direction (Y direction). LEDs, organic electroluminescence (EL) devices (elements), laser devices, or the like may be used for the light-emitting points. A photosensitive member such as a photosensitive drum is disposed at the light-receiving surface106. In a case where the optical apparatus is to be applied to an image reading apparatus, a document is positioned instead of the light source101, and a photoreceptor sensor (line sensor) such as a CMOS sensor or the like is positioned at the light-receiving surface106instead of a photosensitive member.

The imaging optical system105is a lens array including imaging units102and104which include multiple lens units arrayed in the first direction, and shielding portions103to shield stray light rays. The imaging units102and104are configured having one row in the second direction (Z direction) of a lens row where multiple lens portions of the same shape are arrayed at equal intervals in the first direction, as illustrated inFIG. 1C. Hereinafter, the lens portions in imaging units102and104which are disposed on the same optical axis will be collectively described as lens optical system105a.

Lens surfaces102a,102b,104a, and104bof the lens optical system105aall have anamorphic aspheric forms (anamorphic surfaces). The shielding portions103serve to allow, of the light rays passing through the imaging unit102, light rays that contribute to imaging to pass through, and shield stray light rays not contributing to imaging. In the following description, the thickness (width in second direction) of the shielding portions103is excluded from consideration.

The lens portions of the imaging unit102condense the multiple light rays emitted from the light source101on an intermediate imaging plane A in the first cross-section (X-Y cross-section) parallel to the first direction and the optical axis direction of the lens optical system105aas illustrated inFIG. 1A. Note that the intermediate imaging plane A is an imaginary plane where the imaging unit102forms an intermediate image of the light source101(object plane), i.e., performs intermediate imaging of the object plane. The intermediate imaging plane A exists at an approximately intermediate position between the light source101and the light-receiving surface106(image plane). Light rays temporarily condensed at the intermediate imaging plane A enter each lens portion of the imaging unit104, and further are condensed at the light-receiving surface106. That is to say, the imaging unit104forms an image of the intermediate image of the light source101on the light-receiving surface106. In other words, the intermediate image is re-imaged upon the light-receiving surface106.

Thus, the imaging optical system105according to the present embodiment (lens optical system105a) is a system performing erecting same-size imaging of the light-emitting points on the light-receiving surface106, in the X-Y cross-section, i.e., is an erecting same-size imaging system. On the other hand, in the second cross-section (Z-X cross-section) perpendicular to the first direction, the imaging optical system105(lens optical system105a) is a system performing inverted same-size imaging of the light-emitting points on the light-receiving surface106without performing intermediate imaging, i.e., is an inverted same-size imaging system, as illustrated inFIG. 1B. While countless light rays actually are being condensed by the imaging units102and104, only a few characteristic light rays are illustrated inFIG. 1A.

Properties of the imaging optical system105according to the present embodiment are shown in Table 1.

TABLE 1Aspheric formConfigurationLens surfaceLens surfaceLens surfaceLens surfaceResolutiondpi600102a102b104b104aWavelengthλ(nm)780R0R0R0R0Refractive indexn(λ = 780 nm)1.486k0k0k0k0F-No. in first direction of lensFno_m3.90A200.50277A20−0.82549A200.82549A20−0.50277unitF-No. in second direction of lensFno_s1.30A40−0.51259A400.29164A40−0.29164A400.51259unitPower in first direction of lensβm-0.45A60−0.24716A60−0.55971A600.55971A600.24716unitArray pitch in first direction ofp(mm)0.77A800.08357A80−0.01894A800.01894A80−0.08357lens unitNumber of optical systemsNm(count)291A100−6.91825A100−0.78249A1000.78249A1006.91825arrayed in first direction of lensunitNumber of optical systemsNs(count)1A020.15643A02−0.19504A020.19504A02−0.15643arrayed in second direction oflens unitMaximum object height of whichL(mm)0.768A22−0.15873A220.09481A22−0.09481A220.15873lens unit can intake lightSize of light-emitting point inDm(um)42.30A42−0.15055A42−0.30023A420.30023A420.15055first directionSize of light-emitting point inDs(um)25.40A625.65920A623.06561A62−3.06561A62−5.65920second directionAperture sizeA82−13.83601A82−6.53977A826.53977A8213.83601Aperture size in first direction ofAm1(mm)0.7A04−0.03679A04−0.00756A040.00756A040.03679imaging unit 102Aperture size in secondAs1(mm)244A240.14799A240.03211A24−0.03211A24−0.14799direction of imaging unit 102Aperture size in first direction ofAm2(mm)0.7A44−1.03706A44−0.59005A440.59005A441.03706imaging unit 104Aperture size in secondAs2(mm)2.44A64−1.89450A64−0.69876A640.69876A641.89450direction of imaging unit 104PlacementA060.01270A060.00111A06−0.00111A06−0.01270Distance between light sourced1(mm)2.65A26−0.07715A26−0.00101A260.00101A260.07715101 and lens surface 102aDistance between lens surfaced2(mm)1.25A460.97142A460.41327A46−0.41327A46−0.97142102a and lens surface 102bDistance between lens surfaced3(mm)2.16A08−0.00611A08−0.00105A080.00105A080.00611102b and lens surface 104aDistance between lens surfaced4(mm)1.25A28−0.01342A28−0.01827A280.01827A280.01342104a and lens surface 104bDistance between lens surfaced5(mm)2.65A0100.00128A0100.00010A010−0.00010A010−0.00128104b and light-receiving surface106

If we say that the intersection with the optical axis (X axis) at each lens portion of the imaging optical system105is the origin, the axis orthogonal to the optical axis in the first direction is the Y axis, and the axis orthogonal to the optical axis in the second direction is the Z axis, the aspheric form of each lens surface is expressed by the following Expression (1), where R represents the radius of curvature, k represents the conical constant, and Aij(i=0, 1, 2, 3, 4, 5 . . . , j=0, 1, 2, 3, 4, 5 . . . ) is aspheric constants.

A method to design the optical apparatus according to the present embodiment will be described with reference toFIG. 2.

FIG. 2is a conceptual diagram illustrating images (200aand200b) of two adjacent light-emitting points, formed on the light-receiving surface106, to evaluate resolution as Pi. The interval between the two images is set to 1/Pi. ΔxiinFIG. 2represents the distance from the light-receiving surface106where the two images200aand200bbegin to overlap due to defocusing (defocus tolerance value), which indicates a half-value of the depth of field when the contrast is 100%. To say that “contrast is 100%” means contrast when the two images200aand200bdo not overlap, and are completely separated (resolved).

Also, θiis the half-value of the angle of divergence (aperture angle) of the optical fluxes forming the images (imaging fluxes). We can see fromFIG. 2that the half-value of the angle formed between the light ray on the extreme periphery of the multiple light rays making up the imaging optical flux forming the image200a, and the light ray on the extreme periphery of the multiple light rays making up the imaging optical flux forming the image200b, is also θi. Diis the size of the images200aand200bformed on the light-receiving surface106. Note that the parameters inFIG. 2represent a parameter within the X-Y cross-section when the suffix i=m, and represent a parameter within the Z-X cross-section when the suffix i=s.

The following relationship is derived fromFIG. 2for the parameters, such as shown in the following Expression (2).

Transforming Expression (2) yields the defocusing tolerance value Δxiwhen contrast is 100%, shown in the following Expression (3).

Piand Diare decided by the printing dot size set at the image forming apparatus (or image reading apparatus) into which the optical apparatus information has been built, and accordingly are constant for each apparatus model and each printing mode. Also, the light available efficiency of the imaging optical system105is proportionate to the half-value θiof the angle of divergence (aperture angle) of the imaging optical flux, and accordingly is approximately proportionate to tan θi. We can further see from Expression (3) that Δxiis inversely proportionate to tan θi. Thus, we can see that light available efficiency and depth of field are in an inversely proportionate relationship.

Let us consider making the depth of field at each of the X-Y cross-section and Z-X cross-section approximately equal, in order to ensure resolution within both cross-sections and also to realize both light available efficiency and imaging capabilities. Making the depth of field at each of the X-Y cross-section and Z-X cross-section approximately equal means satisfying the following conditional Expression (4).

Substituting Expression (3) into Expression (4) yields the following conditional Expression (5).

The aperture size of the lens optical systems105ain the first and second directions have been designed in the present embodiment so as to satisfy Expression (5). Accordingly, the depth of field in both the X-Y cross-section and Z-X cross-section can be kept from becoming unnecessarily high as to the common depth of field. That is to say, an optimal optical configuration can be achieved to realize both light available efficiency and imaging capabilities (resolution) in both cross-sections.

The range of values in Expressions (4) and (5) will be described here. Normally, if change in astigmatic difference occurs due to error in placement of members of the optical apparatus, the common depth of field can drop as much as 20% or so. The effects of placement error of the members making up the optical apparatus differ depending on whether within the X-Y cross-section or within the Z-X cross-section, so the configuration is preferably designed with this difference in mind, such that the common depth of field has some leeway.

Accordingly, the optical apparatus according to the present embodiment is configured so that the ratio between Δxsand Δxmis contained within a range of 0.8 to 1.2 as shown in Expressions (4) and (5), taking the effects of placement error and so forth into consideration. When the ratio between Δxsand Δxmfalls out of the range of Expressions (4) and (5), the difference in depth of field between the X-Y cross-section and Z-X cross-section becomes great, so good imaging capability while securing light available efficiency at both cross-sections cannot be achieved. Further, if the effects of placement error can be maximally suppressed, a configuration satisfying the following Expression (6) is even more desirable.

Next, change in the depth of field at each light-emitting point will be described. First, the behavior of each light-emitting point of the light source101being imaged on the light-receiving surface106by the imaging optical system105in the X-Y cross-section will be described with reference toFIGS. 3A and 3B.

FIG. 3Ais a diagram illustrating the way in which a light-emitting point101asituated on the optical axis of one lens optical system105a(hereinafter, referred as “at axial object height”) is imaged on the light-receiving surface106in the X-Y cross-section. Light rays emitted from the light-emitting point101aare temporarily condensed at the intermediate imaging plane A by way of the imaging unit102, and subsequently condensed on the light-receiving surface106by way of the imaging unit104. At this time, the light rays emitted from the light-emitting point101aeach only pass through one lens portion at each of the imaging units102and104. That is to say, in the X-Y cross-section, the number of lens optical systems105awhich the light rays emitted from the light-emitting point at axial object height pass through is one. Note that the half-value of the incident angle of an extreme periphery light ray107maof the light rays passing through that lens optical system105awhen entering the light-receiving surface106, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point101a, is θmaof 7.32 degrees.

On the other hand,FIG. 3Bis a diagram illustrating the way in which a light-emitting point101bof which light passes through an intermediate position between optical axes of adjacent lens optical systems105a(hereinafter, referred as “at intermediate object height”) is imaged on the light-receiving surface106in the X-Y cross-section. Light rays emitted from the light-emitting point101bare temporarily condensed at the intermediate imaging plane A by way of the imaging unit102, and subsequently condensed on the light-receiving surface106by way of the imaging unit104, in the same way as with the light rays emitted from the light-emitting point101a. At this time, the light rays emitted from the light-emitting point101bpass through two lens portions at each of the imaging units102and104. That is to say, in the X-Y cross-section the number of lens optical systems105awhich the light rays emitted from the light-emitting point at intermediate object height pass through is two. Note that the half-value of the incident angle of an extreme periphery light ray107mbof the light rays passing through that lens optical system105awhen entering the light-receiving surface106, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point101b, is θmbof 13.46 degrees.

Thus, the number of lens optical systems105awhich the light rays emitted from the light-emitting points pass through in the X-Y cross-section differ according to the position of the light-emitting point, so the half-value θmof the angle of divergence of the imaging optical flux also changes in accordance with the position of the light-emitting point. Note that the maximum (greatest) number of lens optical systems105ato pass through is for the imaging optical flux emitted from a light-emitting point at intermediate object height (light-emitting point101b). That is to say, the half-value θmof the angle of divergence of the imaging optical flux formed by light rays from a light-emitting point at intermediate object height (light-emitting point101b) can be deemed to be the greatest (maximum value). Accordingly, the depth of field for an imaging optical flux emitted from a light-emitting point at intermediate object height is the smallest of the light-emitting points of the light source101.

To be precise, the half-value θmof the angle of divergence of the imaging optical flux from a light-emitting point at intermediate object height (light-emitting point101b) is not the maximum. However, the half-value θmof the angle of divergence of the imaging optical flux is almost completely decided by the number of lens optical systems105athrough which the imaging optical flux passes, so we can view difference due to the position of light-emitting points being non-existent if the number of thereof is the same. Accordingly, the half-value θmof the angle of divergence of the imaging optical flux from a light-emitting point at intermediate object height (light-emitting point101b) is deemed to be the maximum of the multiple light-emitting points in the light source101in the present embodiment.

Next, the behavior of each light-emitting point of the light-emitting point101aand light-emitting point101bbeing imaged on the light-receiving surface106by the imaging optical system105in the Z-X cross-section section will be described with reference toFIGS. 3C and 3D.

Light rays emitted from the light-emitting point101abecome approximately parallel light by way of the imaging unit102, and then are input to the imaging unit104and condensed on the light-receiving surface106, as illustrated inFIG. 3C. The imaging optical system105here is an inverted same-size imaging system in the Z-X cross-section, so the number of lens rows of the lens optical system105awhich light rays emitted from the light-emitting point101apass through is one. In the present embodiment, the number of lens rows in the second direction is one row, so light rays emitted from the light-emitting point101aonly pass through one lens optical system105a. Note that the half-value of the incident angle of an extreme periphery light ray107saof the light rays passing through that lens optical system105awhen entering the light-receiving surface106, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point101a, is θsaof 21.14 degrees.

Light rays emitted from the light-emitting point101bbecome approximately parallel light by way of the imaging unit102, and then are input to the imaging unit104and condensed on the light-receiving surface106, as illustrated inFIG. 3D. Accordingly, light rays emitted from the light-emitting point101balso only pass through one lens optical system105a, in the same way as with light rays emitted from the light-emitting point101a. Note that the half-value of the incident angle of an extreme periphery light ray107sbof the light rays passing through that lens optical system105awhen entering the light-receiving surface106, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point101b, is θsbof 21.14, the same as with θsa.

Thus, the number of lens optical systems105awhich the light rays emitted from the light-emitting points pass through in the Z-X cross-section do not differ according to the position of the light-emitting point with the present embodiment, so the half-value θsof the angle of divergence of the imaging optical flux is constant regardless of the position of the light-emitting point. That is to say, the depth of field is constant regardless of the position of the light-emitting point.

Thus, in the optical apparatus according to the present embodiment, the depth of field changes at each light-emitting point position in the X-Y cross-section, and the depth of field is constant regardless of the position of the light-emitting point in the Z-X cross-section.

Let us now consider whether the depth of field should be made equal (made the same) between the X-Y cross-section and Z-X cross-section at the time of any light-emitting point at the light source101being imaged by the imaging optical system105, taking the difference in depth of field at each light-emitting point that has been described above.

FIGS. 4A and 4Bare diagrams for describing two patterns of making the depth of field the same.FIGS. 4A and 4Billustrates defocusing tolerance values corresponding to each light-emitting point in the X-Y cross-section, connected by dotted lines −Δxmand +Δxm, and illustrates defocusing tolerance values corresponding to each light-emitting point in the Z-X cross-section, connected by solid lines −Δxsand +Δxs. That is to say, the intervals between the dotted lines −Δxmand +Δxmindicate the depth of field in the X-Y cross-section as to each light-emitting point, and the intervals between the solid lines −Δxsand +Δxsindicate the depth of field in the Z-X cross-section as to each light-emitting point. As can be understood fromFIGS. 4A and 4B, the depth of field in the X-Y cross-section changes at each light-emitting point position, while the depth of field in the Z-X cross-section is constant regardless of light-emitting point position.

FIG. 4Ais a pattern where the depth of field in the X-Y cross-section and the depth of field in the Z-X cross-section have been made the same at light-emitting point positions where the depth of field in the X-Y cross-section is the maximum. At this time, the common depth of field is equal to the narrowest depth of field in the X-Y cross-section, so light available efficiency is lost only regarding the difference between the common depth of field and the narrowest depth of field in the X-Y cross-section. On the other hand,FIG. 4Bis a pattern where the depth of field in the X-Y cross-section and the Z-X cross-section have been made the same at light-emitting point positions where the depth of field in the X-Y cross-section is the narrowest. At this time, the common depth of field is equal to the narrowest depth of field in the X-Y cross-section and the narrowest depth of field in the Z-X cross-section, so light available efficiency is lost only regarding the difference between the common depth of field and the widest depth of field in the X-Y cross-section.

The amount of loss in light available efficiency is the same between the two patterns illustrated inFIGS. 4A and 4B. That is to say, the depth of field in the Z-X cross-section can be made narrower with the pattern illustrated inFIG. 4B, as compared to the pattern illustrated inFIG. 4A, which is advantageous regarding imaging capabilities. Accordingly, the optical apparatus according to the present embodiment is designed such that the depth of field is approximately the same in the X-Y cross-section and Z-X cross-section when the depth of field is narrowest in X-Y cross-section, i.e., when the light-emitting points at intermediate object height in the lens optical system105aare imaged on the light-receiving surface106.

As described above, the depth of field is smallest in the present embodiment when light-emitting points in intermediate object height are imaged on the light-receiving surface106. At this time, the half-value θmof the maximum value of the angle of divergence of the imaging optical flux in the X-Y cross-section is 13.46 degrees, and the half-value θsof the maximum value of the angle of divergence of the imaging optical flux in the Z-X cross-section is 21.14 degrees. Also note that the imaging optical system105according to the present embodiment forms same-size images of each of the light-emitting points of the light source101on the light-receiving surface106, in each of the X-Y cross-section and Z-X cross-section. Thus, the image size Dmon the light-receiving surface106in the X-Y cross-section is 42.30 μm which is equal to the size of the light-emitting points, and the image size Dson the light-receiving surface106in the Z-X cross-section is 25.40 μm which is equal to the size of the light-emitting points. Note that resolution P is evaluated as 11.81 lp/mm (equivalent to 600 dpi) in the X-Y cross-section and Z-X cross-section.

Substituting these numerical values into the middle member of conditional Expression (5) yields Expression (7), and we can see that conditional Expression (5) and Expression (6) are satisfied.

FIGS. 5A and 5Bare diagrams illustrating depth properties of the imaging optical system105according to the present embodiment in the X-Y cross-section and in the Z-X cross-section.FIG. 5Aillustrates the relationship between depth of field and contrast when a light-emitting point at axial object height is imaged on the light-receiving surface106. The depth of field in the X-Y cross-section is greater than the depth of field in the Z-X cross-section at each contrast value. On the other hand,FIG. 5Billustrates the relationship between depth of field and contrast when a light-emitting point at intermediate object height is imaged on the light-receiving surface106. The depth of field in the X-Y cross-section and the depth of field in the Z-X cross-section are generally the same at each contrast value.

Table 2 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface106.

Table 2 shows that the depth of field is approximately equal in the X-Y cross-section and in the Z-X cross-section, in the contrast range of 40 to 90%. That is to say, we can see that the depth of field in the X-Y cross-section and in the Z-X cross-section is the same when a light-emitting point at intermediate object height is being imaged on the light-receiving surface106. Thus it has been demonstrated that the optical apparatus according to the present embodiment realizes both light available efficiency and imaging capabilities by satisfying conditional Expression (5). The reason that the ratio of depth of field in the X-Y cross-section and in the Z-X cross-section differs from the numerical value in Expression (7) is that the numerical value in Expression (7) is a theoretical value, and in reality there is error due to influence of aberration and the like in the imaging optical system105.

Note that as described above, conditional Expression (5) has been derived taking into consideration the depth of field when contrast is 100%, so from that perspective, confirmation should be made that the depth of field is the same (approximately equal) in both cross-sections at contrast of 100%. However, as mentioned earlier, confirming at contrast of 100% is difficult, due to aberration of the imaging optical system105not being taken into consideration. Accordingly, in a case of applying conditional Expression (5) to an optical apparatus, the ratio of depth of field in both cross-sections is preferably evaluated at contrast of 80 to 90%, taking into consideration the effects of aberration of the imaging optical system105.

Also, what is demanded of actual image forming apparatuses (and image reading apparatuses) is depth of field evaluated at contrast of 40 to 80%. While conditional Expression (5) has been derived taking into consideration depth of field at contrast of 100%, this can be applied to depth of field at contrast of 40 to 80%, approximatively.

As described above, the optical apparatus according to the present embodiment can provide good imaging capability while securing light available efficiency, by making the depth of field at the time of the imaging optical system105imaging light-emitting points at intermediate object height on the light-receiving surface106to be approximately equal in the X-Y cross-section and in the Z-X cross-section.

Now, description will be made regarding a conditional expression taking into consideration the maximum number of lens optical systems105athrough which light rays from one light-emitting point of the light source101pass. Since the number of lens optical systems105athrough which light rays pass in the Z-X cross-section do not change with the present embodiment, we will consider only the maximum number of lens optical systems105athrough which light rays from one light-emitting point pass in the X-Y cross-section.

The maximum number of lens optical systems105athrough which light rays from one light-emitting point pass is can be expressed by nm=1+integer portion (2×L/p), where L represents the maximum object height regarding which one lens optical system105acan take in light rays, and p represents the array pitch of lens optical systems. In the case that nmis an odd number, the half-value θmof the angle of divergence is the greatest (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface106when nmis an even number. Accordingly, the value of the maximum half-value θmof the angle of divergence of the imaging optical flux changes according to the value of nm.

Now, tan θmin the X-Y cross-section described above is expressed as in the following Expression (8), by the array pitch p in the first direction of the lens optical systems105a, the maximum value nmof the number of lens optical systems105athrough which light rays pass, and distance l between the imaging unit104and light-receiving surface106.

Also, tan θsin the Z-X cross-section is expressed as in the following Expression (9), by the maximum effective width (valid width) T of the imaging optical system105in the second direction, and distance l between the imaging unit104and light-receiving surface106.

Now, the maximum effective width T of the imaging optical system105in the second direction is the maximum width of the region which imaging optical fluxes pass through at the light-emitting points in the second direction. The maximum effective width T of the imaging optical system105in the second direction is equal to the aperture width (aperture size) in the second direction of the lens optical systems105a, in a configuration where only one lens row is arrayed in the second direction, as with the imaging optical system105according to the present embodiment.

Expression (5) can be transformed as Expression (10) by Expressions (8) and (9).

The array pitch p, the maximum number nmof lens optical systems105athrough which light rays from one light-emitting point pass, and the maximum effective width T of the imaging optical system105in the second direction, are set with the present embodiment so as to satisfy Expression (10). Thus, the depth of field in the X-Y cross-section and in the Z-X cross-section can be made approximately equal. Further, satisfying the next Expression (11) is even more preferable, in order to suppress reduction in stability of imaging capabilities to 15%.

The array pitch p of the lens optical systems105ais 0.77 mm in the present embodiment, and the maximum effective width T of the imaging optical system105in the second direction is 2.44 mm, which is equal to the aperture size of the lens optical system105a. Also, the maximum number nmof lens optical systems105athrough which light rays from one light-emitting point pass is two, taking into consideration light rays from light-emitting points at intermediate object height where depth of field is minimal. The values of Piand Diare as described above. Substituting these values into the middle member of Expression (10) yields the following Expression (12), so it can be seen that conditional Expressions (10) and (11) are satisfied.

The values of the middle member differ slightly between Expressions (12) and (7), but this is because Expression (8) includes approximation, and there is no difference in the fundamental idea.

As described above, the lens optical systems of the lens optical systems of the optical apparatus according to the present embodiment are designed so as to satisfy Expressions (5) or (6), or Expressions (10) or (11). Thus, the depth of field at the time of light-emitting points at intermediate object height being imaged on the light-receiving surface106is approximately equal in the X-Y cross-section and in the Z-X cross-section, thereby achieving good imaging capabilities while securing light available efficiency.

Second Embodiment

Next, an optical apparatus according to a second embodiment of the present invention will be described in detail. Components which are the same as or equivalent to those in the first embodiment will be denoted with the same reference numerals, and description thereof simplified or omitted.

The present embodiment differs from the first embodiment with regard to the size of each of the light-emitting points of the light source101, and the aperture size of the lens portion which the imaging unit104has, in the Z-X cross-section. Specifically, the optical apparatus according to the present embodiment is of a configuration where the size of the light-emitting points of the light source is equal in the X-Y cross-section and in the Z-X cross-section, i.e., the resolution in both cross-sections is equal, and also the aperture size Asof the lens portion at the imaging unit104is changed as compared to that in the first embodiment.

At this time, the imaging optical system105according to the present embodiment is of a configuration to perform same-size imaging in the X-Y cross-section and in the Z-X cross-section, so the size of the image formed on the light-receiving surface106by light rays from each of the light-emitting points is the same in the X-Y cross-section and in the Z-X cross-section. That is to say, Dm=Dsholds, and also Pm=Psholds, so the above-described conditional Expression (5) and Expression (10) are as in the following Expressions (13) and (14).

The aperture size Asin the second direction at the imaging units, i.e., the maximum effective width T of the imaging optical system105in the second direction, is 1.70 mm in the present embodiment. Accordingly, the maximum value of the maximum half-value θsof the angle of divergence of the imaging optical flux in the Z-X cross-section, at the time of input of light rays from light-emitting points at intermediate object height to the light-receiving surface106, is 15.07 degrees. At this time, the other values, such as the maximum number nmof lens optical systems105athrough which light rays from one light-emitting point pass, are unchanged from the first embodiment. Accordingly, substituting these values into the middle member of Expressions (13) and (14) yields the following Expressions (15 and 16), and it can be seen that the conditional Expressions (13) and (14) are satisfied.

FIGS. 6A and 6Bare diagrams illustrating depth properties of the imaging optical system105according to the present embodiment in the X-Y cross-section and in the Z-X cross-section, in the same way as withFIGS. 5A and 5B.FIG. 6Aillustrates the relationship between depth of field of light rays from a light-emitting point at axial object height, and contrast, and in the same way as withFIG. 5A, the depth of field in the X-Y cross-section is greater than the depth of field in the Z-X cross-section at each contrast value. On the other hand,FIG. 6Billustrates that the depth of field in the X-Y cross-section and in the Z-X cross-section is approximately equal, due to the relationship between depth of field and contrast, with regard to light rays from a light-emitting point at intermediate object height.

Table 3 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface106.

Table 3 shows that the depth of field is approximately equal in the X-Y cross-section and in the Z-X cross-section, in the contrast range of 40 to 90%. Thus it has been demonstrated that the optical apparatus according to the present embodiment can make the depth of field in the X-Y cross-section and in the Z-X cross-section to be the same when a light-emitting point at intermediate object height is being imaged on the light-receiving surface106, by being configured so as to satisfy conditional Expression (5) and conditional Expression (10).

Thus, good imaging capabilities can be achieved while securing light available efficiency with the optical apparatus according to the present embodiment, regardless of parameter values such as light-emitting point size and so forth.

Third Embodiment

Next, an optical apparatus according to a third embodiment of the present invention will be described in detail. Components which are the same as or equivalent to those in the first embodiment will be denoted with the same reference numerals, and description thereof simplified or omitted.

The present embodiment differs from the first embodiment with regard to the values of the maximum object height L regarding which one lens optical system can take in light rays, and the array pitch p of the imaging optical system. Properties of the imaging optical system according to the present embodiment are shown in Table 4.

TABLE 4Aspheric formConfigurationLens surfaceLens surfaceLens surfaceLens surfaceResolutiondpi600702a702b704b704aWavelengthλ(nm)620R0R0R0R0Refractive indexn(λ = 620 nm)1.534k0k0k0k0F-No. in first direction of lensFno_m3.90A200.50277A20−0.82549A200.82549A20−0.50277unitF-No. in second direction ofFno_s1.30A40−0.51259A400.29164A40−0.29164A400.51259lens unitPower in first direction of lensβm−0.45A60−0.24716A60−0.55971A600.55971A600.24716unitArray pitch in first direction ofp(mm)0.76A800.08357A80−0.01894A800.01894A80−0.08357lens unitNumber of optical systemsNm(count)291A100−6.91825A100−0.78249A1000.78249A1006.91825arrayed in first direction of lensunitNumber of optical systemsNs(count)1A020.15643A02−0.19504A020.19504A02−0.15643arrayed in second direction oflens unitMaximum object height ofL(mm)0.873A22−0.15873A220.09481A22−0.09481A220.15873which lens unit can intake lightsize of light-emitting pointDm(um)42.30A42−0.15055A42−0.30023A420.30023A420.15055in first directionsize of light-emitting point inDs(um)25.40A625.65920A623.06561A62−3.06561A62−5.65920second directionAperture sizeA82−13.83601A82−6.53977A826.53977A8213.83601Aperture size in first directionAm1(mm)0.76A04−0.03679A04−0.00756A040.00756A040.03679of imaging unit 702Aperture size in secondAs1(mm)244A240.14799A240.03211A24−0.03211A24−0.14799direction of imaging unit 702Aperture size in first directionAm2(mm)0.76A44−1.03706A44−0.59005A440.59005A441.03706of imaging unit 704Aperture size in secondAs2(mm)2.44A64−1.89450A64−0.69876A640.69876A641.89450direction of imaging unit 704PlacementA060.01270A060.00111A06−0.00111A06−0.01270Distance between light sourced1(mm)2.65A26−0.07715A26−0.00101A260.00101A260.07715701 and lens surface 702aDistance between lens surfaced2(mm)1.25A460.97142A460.41327A46−0.41327A46−0.97142702a and lens surface 702bDistance between lens surfaced3(mm)2.16A08−0.00611A08−0.00105A080.00105A080.00611702b and lens surface 704aDistance between lens surfaced4(mm)1.25A28−0.01342A28−0.01827A280.01827A280.01342704a and lens surface 704bDistance between lens surfaced5(mm)2.65A0100.00128A0100.00010A010−0.00010A010−0.00128704b and light-receivingsurface 706

First, the behavior of each light-emitting point of a light source701being imaged on a light-receiving surface706by an imaging optical system705in the X-Y cross-section will be described with reference toFIGS. 7A and 7B.

FIG. 7Ais a diagram illustrating the way in which a light-emitting point701aat axial object height is imaged at the light-receiving surface706in the X-Y cross-section. Light rays emitted from the light-emitting point701aare temporarily condensed at the intermediate imaging plane A by way of the imaging unit702, and subsequently condensed on the light-receiving surface706by way of the imaging unit704. At this time, the light rays emitted from the light-emitting point701apasses through three lens portions at each of the imaging units702and704. That is to say, the number of lens optical systems705awhich the light rays emitted from the light-emitting point at axial object height pass through is three. It can be seen fromFIG. 7Athat a great part of the light rays is input to the lens optical system705aat the middle (i.e., on the axis where the light-emitting point701ais situated), while the amount of light rays input to the two lens optical systems705aon either side of this lens optical system705ais scant.

On the other hand,FIG. 7Bis a diagram illustrating the way in which a light-emitting point701bat intermediate object height is imaged on the light-receiving surface706in the X-Y cross-section. Light rays emitted from the light-emitting point701bare temporarily condensed at the intermediate imaging plane A by way of the imaging unit702, in the same way as with light rays emitted from the light-emitting point701a, and subsequently condensed on the light-receiving surface706by way of the imaging unit704. At this time, the light rays emitted from the light-emitting point701bpass through two lens portions at each of the imaging units702and704. That is to say, the number of lens optical systems705awhich the light rays emitted from the light-emitting point at intermediate object height pass through is two.

Next, the behavior of each light-emitting point of the light-emitting point701aand light-emitting point701bbeing imaged on the light-receiving surface706by the imaging optical system705in the Z-X cross-section section will be described with reference toFIGS. 7C and 7D.

Light rays emitted from the light-emitting point701abecome approximately parallel light by way of the imaging unit702, and then are input to the imaging unit704and condensed on the light-receiving surface706, as illustrated inFIG. 7C. The imaging optical system705here is an inverted same-size imaging system in the Z-X cross-section, so the number of lens rows of the lens optical system705awhich light rays emitted from the light-emitting point701apass through is the number of lens rows in the second direction. In the present embodiment, the number of lens rows in the second direction is one row, so light rays emitted from the light-emitting point701aonly pass through one lens optical system705a. Note that the half-value of the incident angle of an extreme periphery light ray707saof the light rays passing through that lens optical system705awhen entering the light-receiving surface706, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point701a, is θsaof 20.27 degrees.

Also, light rays emitted from the light-emitting point701bbecome approximately parallel light by way of the imaging unit702, and then are input to the imaging unit704and condensed on the light-receiving surface706, as illustrated inFIG. 7D. Accordingly, light rays emitted from the light-emitting point701balso only pass through one lens optical system705a, in the same way as with light rays emitted from the light-emitting point701a. Note that the half-value of the incident angle of an extreme periphery light ray707sbof the light rays passing through that lens optical system705awhen entering the light-receiving surface706, i.e., the half-value of the angle of divergence of the imaging optical flux of the light rays emitted from the light-emitting point701b, is θsbof 20.27 degrees, the same as with θsa.

Now, let us calculate the maximum number of lens optical systems705athrough which light rays from one light-emitting point pass. In the present embodiment, the maximum object height L regarding which one lens optical system705acan take in light rays is 0.87 mm, and the array pitch p of lens optical systems705ais 0.76. At this time, nm(the maximum number of lens optical systems705athrough which light rays from one light-emitting point pass in the X-Y cross-section)=1+integer portion (2×L/p)=3. Note that nmis an odd number, so the half-value θmsof the angle of divergence is the maximum (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface706. Accordingly, the half-value of the incident angle of an extreme periphery light ray707maof the light rays passing through three lens optical systems705ain X-Y cross-section, when entering the light-receiving surface706, is θmaof 20.06 degrees, which is the half-value of the angle of divergence of the imaging optical flux.

On the other hand, as described above, the maximum number of lens optical systems705athrough which light rays from one light-emitting point pass in the Z-X cross-section is nsof one, and the half-value of the angle of divergence of the imaging optical flux in X-Y cross-section, is θsof 20.27 degrees. Also, the aperture size Asof the imaging units in the second direction, i.e., the maximum effective width T of the imaging optical system705in the second direction is 2.44 mm.

Substituting these values into the middle member of Expressions (5) and (10) yield the following Expressions (17) and (18).

That is, it can be seen that the values of Expressions (17) and (18) do not satisfy Expressions (5) and (10).

FIGS. 8A and 8Bare diagrams illustrating depth properties of the imaging optical system705according to the present embodiment in the X-Y cross-section and in the Z-X cross-section, the same as withFIGS. 5A and 5B.FIG. 5Aillustrates the relationship between depth of field and contrast when a light-emitting point at axial object height is imaged on the light-receiving surface706, and in the same way as with the case ofFIG. 5A, the depth of field in the X-Y cross-section is greater than the depth of field in the Z-X cross-section at each contrast value. On the other hand,FIG. 8Billustrates that the depth of field in the X-Y cross-section and in the Z-X cross-section are generally the same, due to the relationship between depth of field and contrast when a light-emitting point at intermediate object height is imaged on the light-receiving surface706.

Table 5 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface706.

Table 5 shows that the depth of field in the X-Y cross-section and in the Z-X cross-section is made approximately equal within the range of contrast of 40 through 90%, even though the values of Expressions (17) and (18) do not satisfy the conditional Expressions (5) and (10).

The reason is that the conditional Expressions (5) and (10) derived assuming depth of field at contrast of 100% were used by approximating as conditional expression assuming depth of field at contrast of 40 to 80%. In the first and second embodiments, the conditional Expressions (5) and (10) could be used approximatively, even in the case of evaluating at contrast of 40 to 80%. However, in a case where that approximation cannot be applied and Expressions (5) and (10) cannot be used, expressions equivalent to Expressions (5) and (10) need to be created assuming a case of performing evaluation with depth of field at contrast of 40% to 80%.

Let us consider the reason that Expressions (5) and (10) cannot be used in a case of evaluating with depth of field at contrast of 40% to 80% in the present embodiment. Light rays from axial object height pass through three lens optical systems705ain the present embodiment. As can be seen fromFIG. 7A, of the three lens optical systems705a, light rays passing through the two lens optical systems705aon the sides are very scant, and almost all of the light rays pass through the one lens optical system705aat the middle. Accordingly, a Δxi′ taking into consideration contrast of 40 to 80% (tolerance range of two adjacent light-emitting points overlapping) has to be set as to light rays passing through the lens optical systems705aon the sides.

FIG. 9illustrates the relation between object height as to a certain lens optical system705aof the imaging optical system705, and light available efficiency. As can be seen fromFIG. 9, the amount of light which can be taken in increases as the object height where the light-emitting point is situated increases, and light rays cannot be taken in from an object height greater than the maximum object height L. Now, in a case of defining Δxiassuming contrast of 100%, an object height where the light rays taken into the lens optical system705aare scant, also has to be taken into consideration. However, in a case of defining Δxi′ assuming contrast of 40 to 80%, the lens optical system705ahas to be deemed to not take in light rays with regard to an object height of which the amount of light is not greater than a predetermined amount.

Accordingly, an effective maximum object height (a valid maximum object height) L′ at which one lens optical system705acan take in light rays, when assuming contrast of 40 to 80%, is defined with the present embodiment. The Δxi′ is then defined from ni′ which is the maximum effective number (valid number) of lens optical systems705athrough which light rays for the object heights at or lower than the effective maximum object height L′, and the half-value θi′ of the effective angle (valid angle) of diversion of the imaging optical flux from each object height at or lower than the effective maximum object height L′.

In a case of assuming contrast of 40 to 80%, the present inventor has found from experience that an effective maximum object height L′=0.85 L can be defined as a general rule, when taking into consideration the light rays contributing to imaging. With the present embodiment, the object height L′=0.85×0.87=0.74 mm, so nm′ (the maximum effective number of lens optical systems705athrough which light rays from one light-emitting point pass in the X-Y cross-section)=1+integer portion (2×0.85 L/p)=2. Note that nm′ is an even number, so the half-value θm′ of the angle of divergence is the maximum (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface706. Accordingly, the half-value of the maximum value of the effective angle of divergence of the imaging optical flux in X-Y cross-section is θm′ of 13.98 degrees.

On the other hand, as described above, the maximum effective number of lens optical systems705athrough which light rays from one light-emitting point pass in the Z-X cross-section is ns′ of one, and the half-value of the maximum effective angle of divergence of the imaging optical flux is θs′ of 21.31 degrees. Also, the aperture size Asof the imaging units in the second direction, i.e., the maximum effective width T of the imaging optical system705in the second direction is 2.44 mm. Replacing the angle of divergence θiwith the effective angle of divergence θi′, and replacing the maximum number nmwith the maximum effective number nm′, and substituting these values into the middle member of Expression (10) yield the following Expressions (19) and (20), so we can see that condition Expressions (5) and (10) are satisfied.

Thus, with the optical apparatus according to the present embodiment, good imaging capabilities can be achieved while securing light available efficiency, by performing settings taking into consideration the effective angle of divergence θi′ or maximum effective number nm′, assuming contrast of 40 to 80%.

Fourth Embodiment

Next, an optical apparatus according to a fourth embodiment of the present invention will be described in detail. Components which are the same as or equivalent to those in the first embodiment will be denoted with the same reference numerals, and description thereof simplified or omitted. The present embodiment differs from the first embodiment in that each lens optical system is an enlarging optical system in Z-X cross-section, and the light-emitting point size in Z-X cross-section and the image on the light-receiving surface are not the same size.

FIGS. 10A through 10Dare schematic diagrams of principal portions of an optical apparatus according to the present embodiment, withFIGS. 10A and 10Billustrating the X-Y cross-section, andFIGS. 10C and 10Dillustrating the Z-X cross-section. The optical apparatus according to the present embodiment includes a light source1001including multiple light-emitting points arrayed on an object plane, and an imaging optical system1005which condenses multiple light rays emitted from the light source1001upon a light-receiving surface (image plane)1006.

The imaging optical system1005is a lens array including multiple lens optical systems1005aarrayed in the first direction, and shielding portions1003to shield stray light rays. The optical systems1005ainclude imaging units1002and1004disposed on the same optical axis. Note that unlike the first embodiment, the lens portions making up the imaging unit1002and the lens portions making up the imaging unit1004are of different shapes. Thus, the imaging optical system1005according to the present embodiment has an enlarging system in the Z-X cross-section. Lens surfaces1002aand1002b, of the imaging unit1002, and1004aand1004b, of the imaging unit1004all have anamorphic aspheric forms (anamorphic surfaces). The aspheric forms thereof are expressed in Expression (1) described above.

Properties of the imaging optical system1005according to the present embodiment are shown in Table 6.

TABLE 6Aspheric formConfigurationLens surfaceLens surfaceLens surfaceLens surfaceResolutiondpi6001002a1002b1004b1004aWavelengthλ(nm)780R0R0R0R0Refractive indexn(λ = 780 nm)1.486k0k0k0k0F-No. in first direction of lensFno_m3.90A200.49353A20−0.84151A200.84151A20−0.49353unitF-No. in second direction ofFno_s1.30A40−0.51152A400.29629A40−0.29629A400.51152lens unitPower in first direction of lensβm−0.45A60−0.58605A60−0.45822A600.45822A600.58605unitArray pitch in first direction ofp(mm)0.77A800.55114A80−2.30492A802.30492A80−0.55114lens unitNumber of optical systemsNm(count)291A100−6.18001A1008.30369A100−8.30369A1006.18001arrayed in first direction oflens unitNumber of optical systemsNs(count)1A020.20133A02−0.23125A020.19949A02−0.03519arrayed in second direction oflens unitMaximum object height ofL(mm)0.768A22−0.25709A220.010385A22−0.02678A220.14680which lens unit can intakelightsize of light-emitting pointDm(um)42.30A420.03333A42−0.41981A420.22126A420.28788in first directionsize of light-emitting point inDs(um)25.40A625.65825A623.25668A62−1.32747A62−2.40382second directionAperture sizeA82−11.79314A82−6.03053A821.49199A8223.62346Aperture size in first directionAm1(mm)0.7A04−0.02012A040.00680A040.00382A040.01535of imaging unit 1002Aperture size in secondAs1(mm)244A240.16833A240.01902A24−0.07111A24−0.19636direction of imaging unit 1002Aperture size in first directionAm2(mm)0.7A44−0.85689A44−0.32633A440.61214A441.36064of imaging unit 1004Aperture size in secondAs2(mm)2.44A64−2.75367A64−1.71326A640.10789A64−5.64660direction of imaging unit 1004PlacementA060.01283A060.00356A060.00032A06−0.00686Distance between lightd1(mm)2.62A26−0.02314A26−0.01182A26−0.01030A260.05265source 1001 and lens surface1002aDistance between lensd2(mm)1.27A460.69981A460.41193A46−0.62041A46−2.47916surface 1002a and lenssurface 1002bDistance between lensd3(mm)2.16A080.00714A080.00306A08−0.00070A08−0.01322surface 1002b and lenssurface 1004aDistance between lensd4(mm)1.27A28−0.00717A280.02039A280.02811A28−0.01344surface 1004a and lenssurface 1004bDistance between lensd5(mm)2.62A010−0.00170A0100.00340A0100.00348A0100.02919surface 1004b and light-receiving surface 1006

FIG. 10Ais a diagram illustrating the way in which a light-emitting point1001aat axial object height in the X-Y cross-section is imaged on the light-receiving surface1006by the imaging optical system1005.FIG. 10Bis a diagram illustrating the way in which a light-emitting point1001bat intermediate object height in X-Y cross-section is imaged on the light-receiving surface1006. Light rays emitted from the light-emitting points1001aand1001bare temporarily condensed at the intermediate imaging plane A by way of the imaging unit1002, and subsequently condensed on the light-receiving surface1006by way of the imaging unit1004.

With the present embodiment as well, the light rays emitted from the light-emitting point1001aeach only pass through one lens optical system1005a, while the light rays emitted from the light-emitting point1001beach pass through lens optical systems1005a. The half-value of the angle of divergence of the light rays emitted from the light-emitting point1001ais θmaof 7.31 degrees, and the half-value of the angle of divergence of the light rays emitted from the light-emitting point1001bis θmbof 13.49 degrees. The half-value θmof the angle of divergence of the optical flux changes depending on the position of the light-emitting point in the X-Y cross-section, so the depth of field differs depending on the position of the light-emitting point.

On the other hand, light rays emitted from the light-emitting points1001aand1001bbecome parallel light by way of the imaging unit1002, and then are input to the imaging unit1004and condensed on the light-receiving surface1006, as illustrated inFIGS. 7C and 7D. The imaging optical system1005here is an inverted same-size imaging system in the Z-X cross-section, so the light rays emitted from each of the light-emitting points1001aand1001bonly pass through one lens optical system1005a. Note that the half-value of the angle of divergence of the imaging optical fluxes of the light rays emitted from the light-emitting points1001aand1001b, is θsaand θsbboth of 17.23 degrees. Thus, in the Z-X cross-section, the half-value θsis constant regardless of the position of the light-emitting points, so the half-value of the incident angle of an imaging optical flux is also constant regardless of the position of the light-emitting points.

As described above, while the depth of field of the imaging optical system1005in the X-Y cross-section differs depending on the position of the light-emitting points, the depth of field in the Z-X cross-section is constant regardless of the position of the light-emitting points. Accordingly, the optical apparatus according to the present embodiment is designed such that the depth of field when light-emitting points at intermediate object height are imaged on the light-receiving surface1006is approximately equal in the X-Y cross-section and in the Z-X cross-section. Thus, the smallest depth of field in the X-Y cross-section and the depth of field in the Z-X cross-section can be made to be approximately equal, so imaging capabilities can be stabilized while securing maximal light.

Now, let us calculate the maximum number of lens optical systems1005athrough which light rays from one light-emitting point pass. In the present embodiment, the maximum object height L regarding which one lens optical system105acan take in light rays is 0.768 mm, and the array pitch p of lens optical systems7005ais 0.77 mm. At this time, nm(the maximum number of lens optical systems1005athrough which light rays from one light-emitting point pass in the X-Y cross-section)=1+integer portion (2×L/p)=2. The maximum effective number nm′ taking contrast of 40 to 80% is nm′=1+integer portion (2×0.85 L/p)=2. Also, nmand nm′ are equal, so advantages of the present invention can be obtained with a configuration satisfying conditional Expressions (5) and (10) in both cases of taking in to consideration contrast of 100% and contrast of 40 to 80%.

In the present embodiment, nmis an even number, so the half-value θmof the angle of divergence is the maximum (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface1006. Accordingly, the half-value of the maximum value of the incident angle of an imaging optical flux in X-Y cross-section is 13.49 degrees. On the other hand, as described above, the maximum number of lens optical systems1005athrough which light rays from one light-emitting point pass in the Z-X cross-section is nsof one, and the half-value of the maximum value of the angle of divergence of the imaging optical flux, is θsof 17.23 degrees. Also, the aperture size Asof the imaging units in the second direction, i.e., the maximum effective width T of the imaging optical system1005in the second direction is 2.44 mm.

The imaging optical system1005according to the present embodiment forms same-size images of each of the light-emitting points of the light source1001on the light-receiving surface1006, in the X-Y cross-section and Z-X cross-section. Thus, the image size Dmon the light-receiving surface1006in the X-Y cross-section is 42.30 μm which is equal to the size of the light-emitting points. On the other hand, the imaging optical system1005performs enlarged imaging of the light-emitting points of the light source1001by a power of 1.3, so image size Dson the light-receiving surface1006in the Z-X cross-section is 33.02 μm which 1.3 times the size of the light-emitting points (25.40 μm). In the same way as with the first embodiment, resolution P is evaluated as 11.81 lp/mm (equivalent to 600 dpi) in the X-Y cross-section and Z-X cross-section.

Substituting these numerical values into the middle member of conditional Expressions (5) and (10) yields Expressions (21) and (22), and we can see that conditional Expression (5) is satisfied but Expression (10) is not.

The reason why the present embodiment does not satisfy conditional Expression (10) is that the imaging optical system1005according to the present embodiment is an enlarging optical system, so approximation in Expression (8) described above does not hold. In this way, conditional Expression (10) cannot be applied unless with an optical system where (8) holds.

FIGS. 11A and 11Bare diagrams illustrating depth of field properties of the imaging optical system1005according to the present embodiment in the X-Y cross-section and in the Z-X cross-section.FIG. 11Aillustrates the relationship between depth of field and contrast when a light-emitting point at axial object height is imaged on the light-receiving surface1006, and in the same way as withFIG. 5A, the depth of field in the X-Y cross-section is greater than the depth of field in the Z-X cross-section at each contrast value. On the other hand,FIG. 11Billustrates that the depth of field in the X-Y cross-section and in the Z-X cross-section is approximately equal, due to the relationship between depth of field and contrast, with regard to light rays from a light-emitting point at intermediate object height.

Table 7 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface1006.

Table 7 shows that the depth of field can be made approximately equal in the X-Y cross-section and in the Z-X cross-section, in the contrast range of 40 to 80%. Thus it has been demonstrated that the depth of field in the X-Y cross-section and in the Z-X cross-section can be made the same when a light-emitting point at intermediate object height is being imaged on the light-receiving surface106, by configuring the optical apparatus according to the present embodiment so as to satisfy conditional Expression (5).

Thus, good imaging capabilities can be achieved while securing light available efficiency with the optical apparatus according to the present embodiment, even if an enlarging optical system.

Fifth Embodiment

Next, an optical apparatus according to a third embodiment of the present invention will be described in detail. Components which are the same as or equivalent to those in the first embodiment will be denoted with the same reference numerals, and description thereof simplified or omitted. The present embodiment differs from the first embodiment with regard to the point that the number of lens optical systems through which optical fluxes emitted from one light-emitting point pass is greater.

FIGS. 12A through 12Dare schematic diagrams of principal portions of an optical apparatus according to the present embodiment, withFIGS. 12A and 12Billustrating the X-Y cross-section, andFIGS. 12C and 12Dillustrating the Z-X cross-section. The optical apparatus according to the present embodiment includes a light source1201including multiple light-emitting points arrayed on an object plane, and an imaging optical system1205which condenses multiple light rays emitted from the light source1201upon a light-receiving surface (image plane)1206.

The imaging optical system1205is a lens array including multiple lens optical systems1205aarrayed in the first direction, and shielding portions1203to shield stray light rays. The optical systems1205ainclude imaging unit1202and1204disposed on the same optical axis. In the same way as with the first embodiment, the imaging units1202and1204each have lens portions of the same form arrayed at equal intervals in the first direction at equal intervals, and the imaging units1202and1204are symmetrical with regard to the optical axis direction. Lens surfaces1202aand1202b, of the imaging unit1202, and1204aand1204b, of the imaging unit1204all have anamorphic aspheric forms (anamorphic surfaces). The aspheric forms thereof are expressed in Expression (1) described above.

Properties of the imaging optical system1205according to the present embodiment are shown in Table 8.

TABLE 8Aspheric formConfigurationLens surfaceLens surfaceLens surfaceLens surfaceResolutiondpi6001202a1202b1204b1204aWavelengthλ(nm)780R0R0R0R0Refractive indexn(λ = 780 nm)1.486k0k0k0k0F-No. in first direction of lensFno_m6.90A200.52414A20−1.27350A201.27350A20−0.52414unitF-No. in second direction ofFno_s1.31A40−2.34636A400.73486A40−0.73486A402.34636lens unitPower in first direction of lensβm−0.24A6015.12691A60−4.60626A604.60626A60−15.12691unitArray pitch in first direction ofp(mm)0.52A80−216.13320A808.52304A80−8.52304A80216.13320lens unitNumber of optical systemsNm(count)221A100−11.14076A100−19.97629A10019.97629A10011.14076arrayed in first direction of lensunitNumber of optical systemsNs(count)1A020.14572A02−1.15192A021.15192A02−0.14572arrayed in second direction oflens unitMaximum object height ofL(mm)1.035A22−0.11646A220.23666A22−0.23666A220.11646which lens unit can intake lightsize of light-emitting pointDm(um)42.30A420.69251A42−0.73229A420.73229A42−0.69251in first directionsize of light-emitting point inDs(um)25.40A62−0.32243A622.60923A62−2.60923A620.32243second directionAperture sizeA820.12245A82−6.69795A826.69795A82−0.12245Aperture size in first directionAm1(mm)0.50A04−0.01460A040.00082A04−0.00082A040.01460of imaging unit 1202Aperture size in secondAs1(mm)2.44A240.06767A24−0.00507A240.00507A24−0.06767direction of imaging unit 1202Aperture size in first directionAm2(mm)0.50A44−0.23917A440.02710A44−0.02710A440.23917of imaging unit 1204Aperture size in secondAs2(mm)2.44A640.62105A64−0.09276A640.09276A64−0.62105direction of imaging unit 1204PlacementA060.00261A06−0.00001A060.00001A06−0.00001Distance between light sourced1(mm)3.30A26−0.02011A260.00010A26−0.00010A260.020111201 and lens surface 1202aDistance between lens surfaced2(mm)0.90A460.08062A46−0.00049A460.00049A46−0.080621202a and lens surface 1202bDistance between lens surfaced3(mm)1.36A08−0.00043A080.00000A080.00000A080.000431202b and lens surface 1204aDistance between lens surfaced4(mm)0.90A280.00334A280.00000A280.00000A28−0.003341204a and lens surface 1204bDistance between lens surfaced5(mm)3.30A0100.00003A0100.00000A0100.00000A010−0.000031204b and light-receivingsurface 1206

FIG. 12Ais a diagram illustrating the way in which a light-emitting point1201aat axial object height in the X-Y cross-section is imaged on the light-receiving surface1206by the imaging optical system1205.FIG. 12Bis a diagram illustrating the way in which a light-emitting point1201bat intermediate object height in X-Y cross-section is imaged on the light-receiving surface1206by the imaging optical system1205. Light rays emitted from the light-emitting points1201aand1201bare temporarily condensed at the intermediate imaging plane A by way of the imaging unit1202, and subsequently condensed on the light-receiving surface1206by way of the imaging unit1204.

The present embodiment differs from the first embodiment with regard to the point that the light rays emitted from the light-emitting point1201apass through three lens optical systems1205a, and the light rays emitted from the light-emitting point1201bpass through four lens optical systems1205a. The half-value of the angle of divergence of the light rays emitted from the light-emitting point1201ais θmaof 11.81 degrees, and the half-value of the angle of divergence of the light rays emitted from the light-emitting point1201bis θmbof 15.59 degrees. The half-value θmof the angle of divergence of the optical flux changes depending on the position of the light-emitting point in the X-Y cross-section, so the depth of field differs depending on the position of the light-emitting point.

On the other hand, in the Z-X cross-section, light rays emitted from the light-emitting points1201aand1201bbecome parallel light by way of the imaging unit1202, and then are input to the imaging unit1204and condensed on the light-receiving surface1206, as illustrated inFIGS. 10C and 10D. The imaging optical system1205here is an inverted same-size imaging system in the Z-X cross-section, so the light rays emitted from each of the light-emitting points1201aand1201bonly pass through one lens optical system1205a. Note that the half-value of the angle of divergence of the imaging optical fluxes of the light rays emitted from the light-emitting points1201aand1201b, is θsaand θsbboth of 22.47 degrees. Thus, in the Z-X cross-section, the half-value θsof the incident angle of an imaging optical flux is constant regardless of the position of the light-emitting points, so the depth of field is also constant regardless of the position of the light-emitting points.

As described above, while the depth of field of the imaging optical system1205in the X-Y cross-section differs depending on the position of the light-emitting points, the depth of field in the Z-X cross-section is constant regardless of the position of the light-emitting points. Accordingly, the optical apparatus according to the present embodiment is designed such that the depth of field when light-emitting points at intermediate object height are imaged on the light-receiving surface1206is approximately equal in the X-Y cross-section and in the Z-X cross-section. Thus, the smallest depth of field in the X-Y cross-section and the depth of field in the Z-X cross-section can be made to be approximately equal, so imaging capabilities can be stabilized while securing maximal light.

Now, let us calculate the maximum number of lens optical systems1205athrough which light rays from one light-emitting point pass. In the present embodiment, the maximum object height L regarding which one lens optical system105acan take in light rays is 1.035 mm, and the array pitch p of lens optical systems1205ais 0.52. Accordingly, nm(the maximum number of lens optical systems1205athrough which light rays from one light-emitting point pass in the X-Y cross-section)=1+integer portion (2×L/p)=4. Also, the maximum number nm′ assuming contrast of 40 to 80%=1+integer portion (2×0.85 L/p)=4. Since nmand nm′ are equal, advantages of the present invention can be obtained with a configuration satisfying conditional Expressions (5) and (10) in both cases of taking into consideration contrast of 100% and contrast of 40 to 80%.

In the present embodiment, nmis an even number, so the half-value θmof the angle of divergence is the maximum (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface1206. At this time, the half-value of the maximum value of the incident angle of an imaging optical flux in X-Y cross-section is 15.59 degrees. On the other hand, as described above, the maximum number of lens optical systems1205athrough which light rays from one light-emitting point pass in the X-Y cross-section is nsof one, and the half-value of the angle of divergence of the imaging optical flux, is θsof 22.47 degrees. Also, the aperture size Asof the imaging units in the second direction, i.e., the maximum effective width T of the imaging optical system1205in the second direction is 2.44 mm.

The imaging optical system1205according to the present embodiment forms same-size images of each of the light-emitting points of the light source1201on the light-receiving surface1206, in each of the X-Y cross-section and Z-X cross-section. Thus, the image size Dmon the light-receiving surface1206in the X-Y cross-section is 42.30 μm which is equal to the size of the light-emitting points. The image size Dson the light-receiving surface1206in the Z-X cross-section is the same 25.40 μm. In the same way as with the first embodiment, resolution P is evaluated as 11.81 lp/mm (equivalent to 600 dpi) in the X-Y cross-section and Z-X cross-section.

Substituting these numerical values into the middle member of conditional Expressions (5) and (10) yields Expressions (23) and (24), and we can see that conditional Expressions (5) and (10) are satisfied.

FIGS. 13A and 13Bare diagrams illustrating depth properties of the imaging optical system1205according to the present embodiment in the X-Y cross-section and in the Z-X cross-section, in the same way as with the first embodiment.FIG. 13Aillustrates the relationship between depth of field and contrast when a light-emitting point at axial object height is imaged on the light-receiving surface1206, and in the same way as withFIG. 5A, the depth of field in the X-Y cross-section is greater than the depth of field in the Z-X cross-section at each contrast value. On the other hand,FIG. 13Billustrates that the depth of field in the X-Y cross-section and in the Z-X cross-section is approximately equal, due to the relationship between depth of field and contrast, when a light-emitting point at intermediate object height is imaged on the light-receiving surface1206.

Table 9 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface1206.

Table 9 shows that the depth of field can be made approximately equal in the X-Y cross-section and in the Z-X cross-section, in the contrast range of 40 to 90%. Thus it has been demonstrated that the depth of field in the X-Y cross-section and in the Z-X cross-section can be made the same when a light-emitting point at intermediate object height is being imaged on the light-receiving surface1206, by configuring the optical apparatus according to the present embodiment so as to satisfy conditional Expressions (5) and (10). Thus, good imaging capabilities can be achieved while securing light available efficiency with the optical apparatus according to the present embodiment, even if the number of lens optical systems through which light rays from each light-emitting point pass, increases.

Note that the power in the X-Y cross-section of each lens optical system has to be increased in accordance with increase in the number of lens optical systems through which light rays from one light-emitting point pass with the present embodiment, but increased power also increases aberration, which is undesirable. Accordingly, nmand nm′ are preferably four or less, taking into consideration the imaging capabilities of the lens optical system.

Sixth Embodiment

Next, an optical apparatus according to a third embodiment of the present invention will be described in detail. Components which are the same as or equivalent to those in the first embodiment will be denoted with the same reference numerals, and description thereof simplified or omitted. The present embodiment is a configuration where the lens optical systems according to the first embodiment have been divided into top and bottom, and one thereof shifted in the first direction by half-pitch of the lens optical systems.

FIGS. 14A through 14Care schematic diagrams of principal portions of an optical apparatus according to the present embodiment.FIG. 14Aillustrates the X-Y cross-section,FIG. 1Billustrates the Z-X cross-section, andFIG. 14Cis a frontal view from the X direction. The optical apparatus according to the present embodiment includes a light source1401including multiple light-emitting points arrayed on an object plane, and an imaging optical system1405which condenses multiple light rays emitted from the light source1401upon a light-receiving surface1406.

The imaging optical system1405is a lens array including multiple lens optical systems1405aarrayed in the first direction, and shielding portions1403to shield stray light rays. The lens optical systems1405ainclude imaging units1402and1404situated on the same optical axis. Unlike the first embodiment, the imaging units1402and1404each include two lens rows in the second direction. Each lens row is configured of multiple lens portions of the same shape being arrayed in the first direction at equal intervals. The two lens rows making up each of the imaging units1402and1404are configured such that the lens row making up each imaging unit in the first embodiment is divided top and bottom and shifted in the first direction by a half-pitch of the lens unit array interval. The imaging unit1402and imaging unit1404are situated symmetrically as to the optical axis direction.

Lens surfaces1402athrough1402dof the imaging unit1402and lens surfaces1404athrough1404dof the imaging unit1404each have anamorphic aspheric forms (anamorphic surfaces). The aspheric forms thereof are expressed in Expression (1) described above.

Properties of the imaging optical system1405according to the present embodiment are shown in Table 10.

TABLE 10Aspheric formConfigurationLens surfaceLens surfaceLens surfaceLens surfaceResolutiondpi6001402a, 1402c1402b, 1402d1404b, 1404d1404a, 1404cWavelengthλ(nm)780R0R0R0R0Refractive indexn(λ = 780 nm)1.486k0k0k0k0F-No. in first direction of lens unitFno_m3.90A200.50277A20−0.82549A200.82549A20−0.50277F-No. in second direction of lensFno_s1.30A40−0.51259A400.29164A40−0.29164A400.51259unitPower in first direction of lens unitβm−0.45A60−0.24716A60−0.55971A600.55971A600.24716Array pitch in first direction of lensp(mm)0.77A800.08357A80−0.01894A800.01894A80−0.08357unitNumber of optical systems arrayedNm(count)291A100−6.91825A100−0.78249A1000.78249A1006.91825in first direction of lens unitNumber of optical systems arrayedNs(count)1A020.15643A02−0.19504A020.19504A02−0.15643in second direction of lens unitMaximum object height of whichL(mm)0.768A22−0.15873A220.09481A22−0.09481A220.15873lens unit can intake lightsize of light-emitting point inDm(um)42.30A42−0.15055A42−0.30023A420.30023A420.15055first directionsize of light-emitting point inDs(um)25.40A625.65920A623.06561A62−3.06561A62−5.65920second directionAperture sizeA82−13.83601A82−6.53977A826.53977A8213.83601Aperture size in first direction ofAm1(mm)0.7A04−0.03679A04−0.00756A040.00756A040.03679imaging unit 1402Aperture size in second direction ofAs1(mm)1.22A240.14799A240.03211A24−0.03211A24−0.14799imaging unit 1402Aperture size in first direction ofAm2(mm)0.7A44−1.03706A44−0.59005A440.59005A441.03706imaging unit 1404Aperture size in second direction ofAs2(mm)1.22A64−1.89450A64−0.69876A640.69876A641.89450imaging unit 1404PlacementA060.01270A060.00111A06−0.00111A06−0.01270Distance between light sourced1(mm)2.65A26−0.07715A26−0.00101A260.00101A260.077151401 and lens surface 1402aDistance between lens surfaced2(mm)1.25A460.97142A460.41327A46−0.41327A46−0.971421402a and lens surface 1402bDistance between lens surfaced3(mm)2.16A08−0.00611A08−0.00105A080.00105A080.006111402b and lens surface 1404aDistance between lens surfaced4(mm)1.25A28−0.01342A28−0.01827A280.01827A280.013421404a and lens surface 1404bDistance between lens surfaced5(mm)2.65A0100.00128A0100.00010A010−0.00010A010−0.001281404b and light-receiving surface1406

FIG. 15Ais a diagram illustrating the way in which a light-emitting point1401aat axial object height in the X-Y cross-section is imaged on the light-receiving surface1406by the imaging optical system1405.FIG. 15Bis a diagram illustrating the way in which a light-emitting point1401bat intermediate object height in Z-X in X-Y cross-section is imaged on the light-receiving surface1406.

Now, the present embodiment differs from the other embodiments described above with regard to the positions of the light-emitting points1401bat intermediate object height. Specifically, the light-emitting points1401bare not situated at intermediate positions between optical axes of lens optical systems1405aadjacent in the first direction (Y direction), but are situated at intermediate positions between optical axes of lens optical systems1405aadjacent in the second direction (Z direction). This is because the lens optical systems1405ahave a configuration of being divided top and bottom and shifted by half-pitch.

Light rays emitted from each of the light-emitting points1401aand1401bare temporarily condensed at the intermediate imaging plane A by way of the imaging unit1402, and subsequently condensed on the light-receiving surface1406by way of the imaging unit1404. The half-values of the angles of divergence of the light rays emitted from the light-emitting points1401aand1401bin the X-Y cross-section are θmaand θmbof 7.32 degrees and 13.38 degrees, respectively.

On the other hand, light rays emitted from the light-emitting points1401aand1401bin the Z-X cross-section become approximately parallel light by way of the imaging unit1402, and then are input to the imaging unit1404and condensed on the light-receiving surface1406, as illustrated inFIGS. 15C and 15D. The half-value of the angle of divergence of the imaging optical fluxes of the light rays emitted from the light-emitting points1401aand1401b, is θsaand θsbboth of 21.14 degrees. Thus, in the Z-X cross-section, the half-value θsis constant regardless of the position of the light-emitting points, so the depth of field is also constant regardless of the position of the light-emitting points.

As described above, while the depth of field of the imaging optical system1405in the X-Y cross-section differs depending on the position of the light-emitting points, the depth of field in the Z-X cross-section is constant regardless of the position of the light-emitting points. Accordingly, the optical apparatus according to the present embodiment is designed such that the depth of field when light-emitting points at intermediate object height are imaged on the light-receiving surface1406is approximately equal in the X-Y cross-section and in the Z-X cross-section. Thus, the smallest depth of field in the X-Y cross-section and the depth of field in the Z-X cross-section can be made to be approximately equal, so imaging capabilities can be stabilized while securing maximal light.

Now, let us calculate the maximum number of lens optical systems1405athrough which light rays from one light-emitting point pass. In a case where Expression (10) is to be applied to a configuration where multiple lens rows are arrayed in the second direction as with the present embodiment, lens rows where light rays on the extreme periphery are input have to be taken into consideration. Accordingly, nm, which is the maximum number of lens optical systems1405athrough which light rays from one light-emitting point pass in the X-Y cross-section, and the aperture size Amof the lens optical system1405ain the first direction, are taken into consideration. Specifically, we will consider application of Expression (10) to a lens row where the value of nm×Amis maximum.

In the present embodiment, the maximum object height L regarding which one lens optical system105acan take in light rays is 0.768 mm, and the array pitch p of lens optical systems1405ais 0.77 mm. At this time, nm(the maximum number of lens optical systems705athrough which light rays from one light-emitting point pass in the X-Y cross-section)=1+integer portion (2×L/p)=2. Also, the maximum effective number nm′ taking contrast of 40 to 80% is nm′=1+integer portion (2×0.85 L/p)=2. Further, the aperture size Amin the first direction is 0.7 mm for both upper and lower lens optical systems1405a, so nm×Am=1.4 mm holds. The value of nm×Amis equal for the upper and lower lens optical systems1405ain the present embodiment, so advantages of the present invention can be obtained with a configuration satisfying conditional Expressions (5) and (10) at either row. Also, nmand nm′ are equal, so advantages of the present invention can be obtained with a configuration satisfying conditional Expressions (5) and (10) in both cases of taking into consideration contrast of 100% and contrast of 40 to 80%.

In the present embodiment, nmis an even number, so the half-value θmsof the angle of divergence is the maximum (maximum value) when an imaging optical flux from a light-emitting point at intermediate object height is input to the light-receiving surface1406. At this time, the half-value of the maximum value of the incident angle of an imaging optical flux in X-Y cross-section is 13.38 degrees. On the other hand, as described above, the maximum number of lens optical systems1405athrough which light rays from one light-emitting point pass in the Z-X cross-section is nsof two, and the half-value of the angle of divergence of the imaging optical flux, is θsof 21.14 degrees. Also, the aperture size Asof the lens optical systems1405afor the upper and lower lens rows is 1.22 mm, so the maximum effective width T of the imaging optical system1405in the second direction is 2.44 mm.

The imaging optical system1405according to the present embodiment forms same-size images of each of the light-emitting points of the light source1401on the light-receiving surface1406, in each of the X-Y cross-section and Z-X cross-section. Thus, the image size Dmon the light-receiving surface1406in the X-Y cross-section is 42.30 μm which is equal to the size of the light-emitting points, and the image size Dson the light-receiving surface1406in the Z-X cross-section is 25.40 μm which is equal to the size of the light-emitting points. In the same way as with the first embodiment, resolution P is evaluated as 11.81 lp/mm (equivalent to 600 dpi) in the X-Y cross-section and Z-X cross-section.

Substituting these numerical values into the middle member of conditional Expressions (5) and (10) yields the following Expressions (25) and (26), and we can see that conditional Expressions (5) and (10) are satisfied.

FIGS. 16A and 16Bare diagrams illustrating depth properties of the imaging optical system1405according to the present embodiment in the X-Y cross-section and in the Z-X cross-section, in the same way as with the first embodiment.FIG. 16Aillustrates the relationship between depth of field and contrast when a light-emitting point at axial object height is imaged on the light-receiving surface1406. Also,FIG. 16Billustrates the relationship between depth of field and contrast when a light-emitting point at intermediate object height of each lens optical system1405ais imaged on the light-receiving surface1406.FIG. 16Billustrates that the depth of field in the X-Y cross-section and in the Z-X cross-section is approximately equal.

Table 11 illustrates the depth of field for each of in the X-Y cross-section and in the Z-X cross-section for each contrast and the ratio thereof, when a light-emitting point at intermediate object height is imaged on the light-receiving surface1406.

Table 11 shows that the depth of field can be made approximately equal in the X-Y cross-section and in the Z-X cross-section, in the contrast range of 70 to 100%. Thus it has been demonstrated that the depth of field in the X-Y cross-section and in the Z-X cross-section can be made the same when a light-emitting point at intermediate object height is being imaged on the light-receiving surface1406, by configuring the optical apparatus according to the present embodiment so as to satisfy conditional Expressions (5) and (10).

Thus, good imaging capabilities can be achieved while securing light available efficiency with the optical apparatus according to the present embodiment, even with a configuration where a lens row is divided top and bottom.

Image Forming Apparatus

FIG. 17is a schematic diagram (Z-X cross-sectional view) of principal portions of a color image forming apparatus33according to an embodiment of the present invention. The color image forming apparatus33is a tandem-type color image forming apparatus, which has four of any one of the optical apparatuses (exposure units) illustrated in the embodiments described above, each exposing the light-receiving surface (photosensitive surface) of photosensitive drums in conjunction. The color image forming apparatus33includes optical apparatuses17,18,19, and20, having one of the configurations illustrated in the embodiments, photosensitive drums21,22,23, and24, serving as image carrying members, developing units25,26,27, and28, a conveying belt34, and a fixing unit37. The optical apparatuses17,18,19, and20are each disposed such that the second direction of the imaging optical systems matches the sub-scanning direction (Z direction) of the photosensitive drums21,22,23, and24, which is the direction of rotation thereof.

InFIG. 17, the color image forming apparatus33receives input of color signals of R (red), G (green), and B (blue), from external equipment35such as a personal computer or the like. These color signals are converted into image signals (dot data) of C (cyan), M (magenta), Y (yellow), and K (black) by a printer controller36within the apparatus, and input to the respective optical apparatuses17,18,19, and20. The printer controller36controls each part of the color image forming apparatus33, besides signal conversion.

Exposure lights29,30,31,32modulated in accordance with the color image signals is emitted from the optical apparatuses17,18,19, and20, respectively. The exposure lights29,30,31,32expose the photosensitive surfaces of the photosensitive drums21,22,23, and24charged by charging rollers omitted from illustration, forming electrostatic latent images on the photosensitive surfaces of each. Subsequently, the electrostatic latent images on the photosensitive surfaces of the photosensitive drums21,22,23, and24developed by respective developing units25,26,27, and28, as toner images. The toner images of each color are transferred by overlaying onto a transfer medium, by a transferring unit omitted from illustration, and then fixed by the fixing unit, thereby completing one fill-color image.

Image Reading Apparatus

Optical apparatuses having a configuration according to any of the embodiments described above may be used in an image reading apparatus. In this case an optical apparatus is configured by a document being positioned at the object face of the imaging optical system, and a photoreceptor unit being positioned at the image plane (light-receiving surface). A line sensor configured of a CCD sensor or CMOS sensor or the like, for example, may be used as the photoreceptor unit. Also, a color digital photocopier may be configured by connecting the image reading apparatus as the above-described external equipment35, to the color image forming apparatus33.

An image reading apparatus can irradiate a document by an illumination unit including a light source, condense optical fluxes (reflected light or transmitted light) on an imaging optical system, and receive light by a sensor face of the photoreceptor unit. At this time, the imaging optical system is positioned such that the second direction thereof matches the direction in which the relative position between the document and the imaging optical system is changed (sub-scanning direction), whereby the document can be sequentially read in the sub-scanning direction.

Note that the illumination unit in the image reading apparatus is not restricted to a light source, an a configuration may be used where external light is guided to the original. Here, the image on the original at the light-receiving surface of the photoreceptor unit which the image reading device has can be conceived as being made up of infinitely small dotes. Accordingly, in a case of applying the above-described Expressions (5) and (10) to an optical apparatus relating to an image reading apparatus, Di=0 can be set and transformation made as with the following Expressions (27) and (28).

Modifications

For example, the embodiments have been described above as configurations where Expression (5) is satisfied by innovating the designed aperture size of the lens portions in the first direction and second direction, but design methods for the optical apparatus to satisfy Expression (5) are not restricted to this. For example, a configuration may be employed where innovation is made regarding size of the light-emitting points of the light source in the first direction and second direction to satisfy Expression (5).

Also, the lens surfaces of the imaging optical system in the embodiments have aspheric forms expressed by Expression (1), but the present invention is not restricted to this, and aspheric forms expressed by other expressions may be employed. Also, while light-emitting points are imaged inverted on the light-receiving surface without intermediate imaging in the Z-X cross-section, the light-emitting points may be imaged erect on the light-receiving surface after intermediate imaging, as with the X-Y cross-section.

Further, configurations where two rows of imaging units are arrayed have been described for the imaging optical system in the embodiments, but the number of imaging units is not restricted thereto, and an imaging optical system may be configured having three or more imaging units. Also, while the imaging unit in the sixth embodiment is of a configuration having two lens rows in the second direction, an imaging unit may be configured having three or more lens rows in the second direction.

Also, while the light source according to the embodiments has been described as a configuration where multiple light-emitting points are arrayed in a first direction alone, a configuration may be employed where multiple rows of the light-emitting points are arrayed in the second direction, and the multiple light-emitting points are arrayed in a staggered layout. This configuration enables a greater number of light-emitting points to be densely arrayed without consideration of space to other light-emitting points adjacent in the first direction, so resolution can be further improved.

The recording density of the above-described image forming apparatus and image reading apparatus is not restricted. However, when taking into consideration that the higher the recording density is, the higher the demanded image quality is, the optical apparatus according to the above-described embodiments exhibits greater advantages in image formation apparatuses of 1200 dpi or higher.

This application claims the benefit of Japanese Patent Application No. 2012-284439, filed Dec. 27, 2012, which is hereby incorporated by reference herein in its entirety.