1. An interferometric scanning method for measuring test optics having aspheric surfaces including those with large departures from spherical, said method comprising the steps of:
generating a first wavefront from a known origin along a scanning axis;
aligning a test optic on the scanning axis and selectively moving it along said scanning axis relative to said known origin so that said first wavefront intersects the test optic at the apex of the aspheric surface and at one or more radial positions where the first wavefront and the aspheric surface intersect at points of common tangency in circular zones around said scanning axis;
interfering the first wavefront with a second wavefront to generate interferograms containing phase information about the differences in optical path length between the center of the test optic and the one or more radial positions;
directing the interferograms onto a detector to provide an electronic signal carrying the phase information;
measuring the axial distance, \u03bd, by which the test optic is moved with respect to said origin;
determining the detector pixel height corresponding to where the first wavefront and test surface slopes match for each scan position;
determining the angles, \u03b1, of the actual normal to the surface of points at each zone as a function of the distance along the scanning axis; and
using the angles, \u03b1, for determining information corresponding to the coordinates axial distance z and radial distance h of the aspheric surface at the common points of tangency.
2. An interferometric scanning method for measuring test optics having aspheric surfaces including those with large departures from spherical, the method comprising the steps of:
generating a first wavefront upstream of a known origin along a scanning axis;
generating a second wavefront upstream of the known origin;
reflecting the first wavefront off an aspherical surface of a test optic that is movable along the scanning axis relative to the known origin;
interfering the first wavefront with the second wavefront to generate interferograms containing phase information about differences in optical path lengths between locations on the test optic away from an apex of the aspherical surface relative to the location of the apex;
directing the interferograms onto a detector to provide an electronic signal carrying the phase information;
evaluating from the interferograms, as a function of an axial distance, \u03bd, along the scanning axis, an angle \u03b1between the scanning axis and a surface normal of the aspherical surface at each of the locations of the test optic having a common tangency with the first wavefront; and
determining, based on \u03b1, information corresponding to the coordinates axial distance z and radial distance h of the aspheric surface at each of the locations.
3. The interferometric scanning method of claim 1, wherein a radius of curvature of the first wavefront impinging on the test optic varies as a function of the axial distance, \u03bd, by which the test optic is moved with respect to the origin.
4. The interferometric scanning method of claim 2, wherein the second wavefront is generated by reflection from at least a partial spherical surface disposed upstream of the origin along the scanning axis.
5. The interferometric scanning method of claim 4, wherein the interferograms contain phase information about differences between the spherical surface and corresponding locations on the aspherical surface of the test optic having common tangency with the first wavefront.
6. The interferometric scanning method of claim 4, wherein the first wavefront passes through the partial spherical surface prior to impinging on the aspherical surface of the test optic.
7. The interferometric method of claim 2, further comprises determining any misalignment of the test optic along the scanning axis.
8. The interferometric method of claim 2, wherein the misalignment of the test optic is differentiated from a coma error of the aspherical surface of the test object.
9. The interferometric scanning method of claim 2 further comprises determining the coordinates z and h of the aspheric surface in a vicinity of the locations having common tangency, wherein an angle \u03b1between the scanning axis and a surface normal of the aspherical surface in the vicinity satisfies \u03b1min\u2266\u03b1\u2266\u03b1max where \u03b1min and \u03b1max are angles whose corresponding detector pixels heights at a scan position \u03bdhave a low fringe density in the interferogram.
10. The interferometric method of claim 2, wherein a shape of the aspherical surface of the test optic is determined by:
recording a first interferogram that includes the phase information about the optical path difference between the apex of the aspherical surface of the test optic and a first location having a common tangency with the apex;
recording a second interferogram that includes phase information at a second location such that the first and second interferograms include phase information from areas of the test optic that are overlapping;
evaluating a mathematical function connecting the phase information measured at the detector to angles \u03b1at the aspherical surface of the test object for each of the interferogram;
optimizing each of the mathematical functions such that an interpolation of a model of the aspherical surface of the test object based on these mathematical functions are substantially identical in the areas of the test surfaces that are overlapping.
11. The interferometric scanning method of claim 2 further comprises reporting the shape of the aspheric surface as a difference between its measured shape and its design shape.
12. The interferometric scanning method of claim 2 wherein the angles, \u03b1, are calculated using optical properties of a system used to direct the interferograms onto the detector.
13. The interferometric scanning method of claim 12 wherein the optical properties used to calculate angles \u03b1comprise a mathematical function that relates pixel height, hpix, in image space to angle \u03b1in object space.
14. The interferometric scanning method of claim 12 wherein the optical properties are determined while measuring an aspheric test surface.
15. Interferometric scanning apparatus for measuring test optics having aspheric surfaces including those with large departures from spherical, the apparatus having a scanning axis and comprising:
a radiation source and optical arrangement for generating first and second wavefronts upstream of a known origin along the scanning axis;
a precision manipulator for aligning a test optic on the scanning axis and selectively moving the test optic an axial distance, \u03bd, with respect to the origin along the scanning axis so that the first wavefront has a radius of curvature that varies as a function of the axial distance \u03bd, as the first wavefront reflects from an aspherical surface of the test optic;
a distance measuring device for measuring the axial distance \u03bd;
a two-dimensional detector;
optics for directing the interferograms onto the detector to provide an electronic signal carrying phase information about differences in optical path lengths between locations of the aspherical surface away from an apex of the aspherical surface relative to the location of the apex; and
a programmable device for:
evaluating from the interferograms, as a function of an axial distance, \u03bd, along the scanning axis, an angle \u03b1between the scanning axis and a surface normal of the aspherical surface at each of the locations having a common tangency with the first wavefront; and
determining, based on \u03b1, information corresponding to the coordinates axial distance z and radial distance h of the aspheric surface at each of the locations.
16. The interferometric scanning apparatus of claim 15, wherein the programmable device evaluates the interferograms by determining a detector pixel height corresponding to locations on the test surface having a slope that match a radius of curvature of the first wavefront at the aspherical surface, at the axial distance \u03bdfor each scan position.
17. The interferometric scanning apparatus of claim 15 wherein said programmable device is further configured to determine the coordinates z and h of the aspheric surface in a vicinity of the locations having common tangency wherein an angle \u03b1between the scanning axis and a surface normal of the aspherical surface in the vicinity satisfies \u03b1min\u2266\u03b1\u2266\u03b1max where \u03b1min and \u03b1max are angles whose corresponding detector pixels heights at a scan position \u03bdhave a low fringe density in the interferogram.
18. The interferometric scanning apparatus of claim 15 wherein the programmable device is further configured to report the shape of the aspheric surface as a difference between its measured shape and its design shape.
19. The interferometric scanning apparatus of claim 15 wherein the optical properties of a system used to direct the interferograms onto the detector is used to calculate angles \u03b1and comprises a mathematical function that relates pixel height, hpix, in image space to the angle \u03b1in object space.
20. The interferometric scanning apparatus of claim 15 wherein the interferometric scanning apparatus has the general form of a Fizeau.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A line image forming method, comprising the steps of:
ejecting a plurality of droplets of liquid sequentially from an inkjet head, the liquid containing a functional component; and
depositing the droplets of the liquid onto a non-permeable medium, the deposited droplets becoming joined together on the non-permeable medium to form a line pattern of the liquid,
wherein a receding contact angle of the liquid with respect to the non-permeable medium being not larger than 10\xb0.
2. The line image forming method as defined in claim 1, wherein a static contact angle of the liquid with respect to the non-permeable medium is not smaller than 10\xb0.
3. The line image forming method as defined in claim 1, wherein in the depositing step, a dot pitch p (\u03bcm) of the deposited droplets which are adjacent to each other on the non-permeable medium is controlled to satisfy:
p
\u2264
\u03c0
\ue89e
\ue89e
d
6
\ue89e
(
\u03b8
sin
2
\ue89e
\u03b8
–
cos
\ue89e
\ue89e
\u03b8
sin
\ue89e
\ue89e
\u03b8
)
\ue89e
{
tan
\ue89e
\u03b8
2
\ue89e
(
3
+
tan
2
\ue89e
\u03b8
2
)
}
–
2
3
,
where d (\u03bcm) is a droplet diameter obtained by spherical conversion of a volume of each of the droplets before being deposited on the non-permeable medium, and \u03b8 (rad) is a static contact angle of the liquid with respect to the non-permeable medium.
4. The line image forming method as defined in claim 1, wherein in the ejecting step, an ejection frequency of the inkjet head is not lower than 1 kHz.
5. The line image forming method as defined in claim 1, wherein:
the liquid is configured to be cured by irradiation of an activating light beam;
in the ejecting step, the inkjet head is controlled in such a manner that a subsequent droplet to be combined with an aggregate of a group of droplets having been previously deposited on the non-permeable medium is deposited onto the non-permeable medium before the aggregate of the group of previously deposited droplets reaches a state of equilibrium on the non-permeable medium; and
the line image forming method further comprises the step of curing the liquid deposited on the non-permeable medium by irradiating the activating light beam onto the liquid on the non-permeable medium.
6. The line image forming method as defined in claim 5, wherein in the curing step, a time T (s) from depositing of a last deposited droplet forming the line pattern until curing of the line pattern is controlled to satisfy:
T
\u2264
(
\u03c0
6
\ue89e
\u03b8
)
3
,
where \u03b8 (rad) is a static contact angle of the liquid with respect to the non-permeable medium.
7. The line image forming method as defined in claim 1, wherein the liquid contains volatile solvent.
8. A line image forming apparatus, comprising:
an inkjet head which ejects a plurality of droplets of liquid containing a functional component;
a movement device which causes the inkjet head and a non-permeable medium to move relatively to each other, the droplets of the liquid ejected from the inkjet head being deposited onto the non-permeable medium; and
a control device which controls the inkjet head and the movement device to form a line pattern of the liquid on the non-permeable medium by ejecting the droplets sequentially from the inkjet head and depositing the droplets onto the non-permeable medium, the deposited droplets having deposition time differences and becoming joined together on the non-permeable medium to form the line pattern of the liquid,
wherein a receding contact angle of the liquid with respect to the non-permeable medium being not larger than 10\xb0.
9. The line image forming apparatus as defined in claim 8, wherein the control device controls the inkjet head to eject the droplets at an ejection frequency of not lower than 1 kHz.
10. The line image forming apparatus as defined in claim 8, wherein:
the liquid is configured to be cured by irradiation of an activating light beam;
the line image forming apparatus further comprises an activating light irradiation device which irradiates the activating light beam onto the liquid deposited on the non-permeable medium to cure the liquid on the non-permeable medium;
the control device controls the inkjet head in such a manner that a subsequent droplet to be combined with an aggregate of a group of droplets having been previously deposited on the non-permeable medium is deposited onto the non-permeable medium before the aggregate of the group of previously deposited droplets reaches a state of equilibrium on the non-permeable medium; and
the control device controls the activating light irradiation device in such a manner that a time T (s) from depositing of a last deposited droplet forming the line pattern until curing of the line pattern satisfies:
T
\u2264
(
\u03c0
6
\ue89e
\u03b8
)
3
,
where \u03b8 (rad) is a static contact angle of the liquid with respect to the non-permeable medium.
11. The line image forming apparatus as defined in claim 10, wherein the control device controls the inkjet head in such a manner that a deposition time interval t (s) of the droplets adjacent to each other on the non-permeable medium satisfies:
t
\u2264
(
\u03c0
6
\ue89e
\u03b8
)
3
\xd7
0.001
.
12. The line image forming apparatus as defined in claim 10, wherein:
the movement device includes a medium conveyance device which conveys the non-permeable medium in a medium conveyance direction at a uniform speed; and
the activating light irradiation device is arranged on a downstream side of the inkjet head in terms of the medium conveyance direction.
13. The line image forming apparatus as defined in claim 10, wherein the activating light irradiation device is attached to the inkjet head, and the inkjet head and the activating light irradiation device are unitedly moved relatively with respect to the non-permeable medium.