CN115128809B - Grating efficiency distribution characterization and optimization method for realizing uniform imaging of holographic waveguide display system - Google Patents
Grating efficiency distribution characterization and optimization method for realizing uniform imaging of holographic waveguide display system Download PDFInfo
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Abstract
The invention discloses a grating efficiency distribution characterization and optimization method for realizing uniform imaging of a holographic waveguide display system. The method comprises the following steps: the holographic waveguide structure is precisely tracked in full view field, the detector element is utilized to obtain two-dimensional graphs of illuminance distribution on the incident grating, the intermediate grating and the emergent grating, points in the grating in two directions parallel to the grating vector and perpendicular to the grating vector are respectively taken to describe main illuminance distribution of the grating, and the distribution of the grating efficiency in each area is utilized to compensate the energy distribution, so that an efficiency distribution curve of the grating is obtained. The peak efficiency distribution of the holographic body grating obtained by the method is optimized for each grating division area, and the problem of uneven out-of-plane illuminance commonly existing in the existing two-dimensional pupil expansion can be solved.
Description
Technical Field
The invention relates to the field of holographic waveguide display, in particular to a grating efficiency distribution characterization and optimization method for realizing uniform imaging of a holographic waveguide display system.
Background
With the development of the micro display industry, display devices are being miniaturized and personalized. In recent years, the head mounted display technology has received a great deal of attention from the market. Head-mounted display devices represented by Augmented Reality (AR) and Virtual Reality (VR) are being developed and applied to the military field and consumer market in a large amount of research.
Conventional near-eye display devices have difficulty in producing a large exit pupil range with a guaranteed large field angle (FOV) due to limitations of optical principles. The waveguide display device utilizes the light rays in the waveguide medium to satisfy the principle of total reflection propagation, and with the help of the optical coupling device, the light rays can be emitted for multiple times in the waveguide propagation process, namely, the larger exit pupil range can be easily achieved by emitting for multiple times at different spatial positions in the waveguide propagation process. At present, more one-dimensional mydriasis and two-dimensional mydriasis are applied, the one-dimensional mydriasis only needs to use two optical coupling elements of incidence and emergence, and only the FOV in the x direction is considered. Three optical coupling elements are needed for two-dimensional pupil expansion, and compared with one intermediate optical coupling element for one-dimensional pupil expansion, light rays can propagate in the y direction, so that a larger out-of-drum area is formed.
The two coherent light beams propagating in the same plane are incident into a photosensitive medium with the thickness d, and interfere inside the medium to form the volume holographic grating. This process is a recording process, and if two coherent light beams are injected from both sides of the photosensitive medium toward each other during recording, a reflection type volume hologram grating is formed. According to the diffraction theory of the grating, to add the phases of the continuous scattered waves and maximize the total diffraction wave amplitude, the wavelength lambda of the incident light in the medium, the included angle theta between the incident light and the grating fringe surface and the grating spacing lambda must meet the Bragg condition. It is known that when a beam of light with the same wavelength is incident on the volume holographic grating in a specific direction, the holographic grating generated by the above-mentioned interferometry automatically satisfies the diffraction phenomenon of the bragg condition. When light with other wavelengths or light enters along other directions, the Bragg condition is not satisfied, and the light beam can penetrate through the holographic grating and does not generate diffraction phenomenon.
The holographic grating has excellent optical characteristics as an excellent optical coupling device, has excellent angle selectivity and wavelength selectivity, and is small in size and light in weight. Wherein most of the ambient light is directly transmitted, i.e. with good transparency, due to its good angular and wavelength selectivity. It is largely used in waveguide Display devices as an optical coupling device to realize a See-through Display. The diffraction efficiency of the holographic grating varies monotonically with the exposure time or the grating thickness within a certain exposure time and grating thickness interval, which is beneficial to regulating and controlling the peak efficiency of the grating, as shown in fig. 1 and 2. By the basic principle of holography, the energy of light rays is reduced by a part every time the light beams strike the grating, the striking-through of the holographic waveguide display is mainly obtained by multiple total reflections of the light beams on the emergent grating, and under the condition of not carrying out efficiency regulation and control, the energy of the light beams is reduced exponentially, so that the light beams are seriously uneven in a certain striking-out range. The human eye must then image the energy convergence in different directions at different locations, resulting in non-uniformity in brightness and color of the viewed image, as shown in fig. 3.
Disclosure of Invention
The invention aims to: in order to overcome the problem of uneven imaging caused by uneven output of a holographic waveguide display system under the condition of two-dimensional pupil expansion, the invention provides a method for representing holographic grating efficiency distribution, and provides a guiding basis for grating partition and grating peak efficiency distribution.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for characterizing grating efficiency distribution for uniformly imaging a holographic waveguide display system, which characterizes illuminance distribution of a grating in a two-dimensional mydriatic structure for holographic waveguide display, wherein the grating includes an incident grating, an intermediate grating and an exit grating; the method comprises the following steps:
step 1: carrying out full-view field ray tracing on a two-dimensional pupil expansion structure displayed by the holographic waveguide;
step 2: obtaining an illuminance distribution two-dimensional graph on the incident grating, the intermediate grating and the emergent grating by using the detector element;
step 3: respectively taking points in two directions parallel to the grating vector and perpendicular to the grating vector in the incident grating, the intermediate grating and the emergent grating to describe the main illuminance distribution of the grating;
step 4: and (3) reversely deducing an efficiency distribution curve which is required to be met by different positions on the grating when the energy distribution on the grating is uniform, so as to compensate the energy loss caused by the reflection of the light beam on the holographic body grating, and ensure that the total reflection and the imaging are uniform.
Specifically, step 3 includes the following:
selecting a first straight line and a second straight line from the incident grating, wherein the first straight line coincides with a grating vector of the incident grating and passes through a center point of the incident grating, and the second straight line is perpendicular to the incident grating vector and passes through the center point of the incident grating;
selecting a third straight line and a fourth straight line from the intermediate grating, wherein the third straight line coincides with the intermediate grating vector and passes through the highest illuminance point of the intermediate grating, and the fourth straight line is perpendicular to the third straight line and passes through the midpoint of the third straight line;
and selecting a fifth straight line and a sixth straight line from the emergent grating, wherein the fifth straight line coincides with the emergent grating vector and passes through an intersection point of the third straight line and the upper boundary of the intermediate grating, the sixth straight line is perpendicular to the fifth straight line, and the fifth straight line passes through the midpoint of the sixth straight line.
Further, the two-dimensional illuminance distribution of the incident grating, the intermediate grating and the emergent grating is discrete, a continuously distributed point set is obtained by smoothing the two-dimensional illuminance distribution in a two-dimensional plane through a mean value algorithm, and then the continuously distributed point set is fitted through a least square method to obtain illuminance distribution curves of the gratings in two linear dimensions.
Wherein the illuminance distribution curve in the grating vector direction in the incident grating, the intermediate grating and the exit gratingThe change trend of the fourth-order polynomial curve shown in the formula (I) is satisfied:
(Ⅰ)：
in the middle of、/>、/>、/>、/>Representing a fourth order polynomial curve fitted by least squares +.>Weighting coefficients of +.>Representing the position coordinates in the direction of the grating vector.
Illuminance distribution curve in direction perpendicular to grating vector in incidence grating, middle grating and emergent gratingThe trend of the sum of three sinusoids shown in the formula (II) is satisfied:
(Ⅱ):
、/>、/>
、/>respectively represent->Distribution of positional relationship->Representing the position coordinates of the raster vector in the vertical direction.
Further, the grating efficiency profile is obtained by the following steps:
integrating the illuminance distribution curves of the two dimensions of the grating to obtain total illuminance;
dividing the total illuminance by the integration interval to obtain average illuminance in the whole range;
dividing the average illumination by the illumination at each location, and multiplying the obtained value by the initial grating efficiency at that location to obtain a new grating efficiency distribution curve.
The calculation formula is as follows:
（Ⅲ）：
wherein,for the grating efficiency profile +.>For the upper and lower limit of the integration position, +.>Peak efficiency for the initial grating; />Is an illuminance distribution curve.
The grating efficiency distribution curves of the incident grating, the intermediate grating and the emergent grating in the grating vector direction have opposite trends with the illuminance distribution curve, and accord with the fourth-order polynomial decreasing trend; the grating efficiency distribution curve in the direction perpendicular to the grating vector accords with the trend that the sum of three sine curves is firstly reduced and then increased.
Further, the grating efficiency profile may be used to direct the beam exposure time or energy, or to direct the thickness variation in making a wedge-shaped holographic volume grating.
Furthermore, the perpendicular grating vector and the grating efficiency distribution curve parallel to the grating vector can bring basis for grating partition of the two-dimensional pupil expansion, and the grating can be selectively segmented along the grating vector or the direction perpendicular to the grating vector or the two directions can be simultaneously segmented. The grating is divided into discrete areas or is continuously graded in these two dimensions.
The beneficial effects are that: compared with the prior method, the invention has the following advantages.
1. At present, the characterization of the grating illuminance distribution starts from a single view field, and the law of the grating illuminance distribution under each view field is found. The method provided by the invention is used for representing the illuminance distribution of the whole grating from the ray trace data of the whole field of view.
2. The characterization method provided by the invention is applicable to two-dimensional pupil expansion structures with different deflection angles, has universality, and has better uniformity on efficiency distribution curves of the incident grating, the intermediate grating and the emergent grating.
3. The grating efficiency distribution curve provided by the invention has simple division of diffraction efficiency and strong practicality.
Drawings
FIG. 1 is a diagram showing the relationship between the thickness and diffraction efficiency of a holographic volume grating;
FIG. 2 is a graph showing the relationship between exposure time and diffraction efficiency at different exposure energies;
FIG. 3 is an imaging diagram of a holographic waveguide display system without zone efficiency control;
FIG. 4 is a schematic diagram of a method for characterizing the grating efficiency distribution of a holographic waveguide display;
FIG. 5 is a schematic diagram of the distribution of points on the fourth straight line 7 in the intermediate grating;
fig. 6 is a schematic diagram of the distribution of points on a sixth straight line 9 in the exit grating;
FIG. 7 is a schematic diagram of a method of grating partitioning;
FIG. 8 is a graph showing the comparison of the front-to-back output uniformity of the grating efficiency zone control.
Detailed Description
The technical scheme of the present invention is explained and illustrated in detail below with reference to the accompanying drawings and specific embodiments.
According to the grating efficiency distribution characterization and optimization method for realizing uniform imaging of the holographic waveguide display system, illumination distribution characterization is carried out on an incident grating 1, an intermediate grating 2 and an emergent grating 3 in a two-dimensional pupil expansion structure of holographic waveguide display, and in the illumination distribution characterization, illumination distribution curves in two directions parallel to a grating vector and perpendicular to the grating vector are selected for the incident grating 1, the intermediate grating 2 and the emergent grating 3 to characterize the overall energy distribution trend, and the illumination distribution trend of the whole grating is uniformly summarized by utilizing the illumination distribution of light rays in two dimensions. And (3) reversely deducing an efficiency distribution curve which is required to be met by different positions on the grating when the energy distribution on the grating is uniform, so as to compensate the energy loss caused by the reflection of the light beam on the holographic body grating, and ensure that the total reflection and the imaging are uniform.
Specifically, the grating illuminance distribution is obtained according to the light ray trace result of the holographic waveguide display system under the full view field. When the illumination distribution trend of the light rays in two dimensions is utilized to uniformly summarize the illumination distribution trend of the whole grating, the selected directions are as follows:
the linear positions of the two selected dimensions in the incident grating 1 are as follows: the first straight line 4 coincides with the grating vector of the incident grating and passes through the center point of the incident grating, and the second straight line 5 is perpendicular to the incident grating vector and also passes through the center point of the incident grating.
The linear positions of the two dimensions selected in the intermediate grating 2 are as follows: the third line 6 coincides with the intermediate grating vector and passes through the highest point of the intermediate grating illuminance, and the fourth line 7 is perpendicular to the incident grating vector and also passes through the midpoint of the third line 6.
The linear positions of the two dimensions selected in the exit grating 3 are as follows: the fifth line 8 coincides with the outgoing grating vector and passes the intersection of the third line 6 and the upper boundary of the intermediate grating, the sixth line 9 is perpendicular to the fifth line (8) and the fifth line 8 passes the midpoint of the sixth line 9.
Wherein, the first straight line 4, the third straight line 6 and the fifth straight line 8 have similar variation trend, and all satisfy the following forms:
(Ⅰ)：
in the middle of、/>、/>、/>、/>Representing a fourth order polynomial curve fitted by least squares +.>Weighting coefficients of +.>Representing the position coordinates in the direction of the grating vector.
The second straight line 5, the fourth straight line 7 and the sixth straight line 9 have similar variation trends, and all satisfy the form of the sum of three sinusoids:
(Ⅱ):
、/>、/>
、/>respectively represent->Distribution of positional relationship->Representing the position coordinates of the raster vector in the vertical direction.
Further, the method for calculating the grating efficiency distribution curve is as follows:
the method comprises the steps of firstly integrating an illuminance distribution curve to obtain total illuminance in the direction, dividing the total illuminance by an integration interval to obtain average illuminance, dividing the average illuminance by the illuminance at each position, and multiplying the obtained value by initial grating efficiency at the position to obtain a new grating efficiency distribution curve. The method improves the low illumination by reducing the high illumination, thereby achieving the compensation effect.
The grating efficiency distribution curve is obtained by processing the illuminance distribution of each grating, thereby realizing the purpose of reducing high illuminance and improving low illuminance and achieving the compensation effect. The calculation method can be summarized as formula (III):
(Ⅲ)：
wherein,for the grating efficiency profile +.>For the upper and lower limit of the integration position, +.>For peak efficiency of the initial grating +.>Is an illuminance distribution curve. Wherein it is noted that the diffraction efficiency +.>Is defined, the maximum diffraction efficiency is 100%.
The grating efficiency distribution curves of the incident grating 1, the intermediate grating 2 and the emergent grating 3 in the grating vector direction have opposite trends with the illuminance distribution curve, and conform to the fourth-order polynomial decreasing trend; the grating efficiency distribution curve in the direction perpendicular to the grating vector accords with the trend that the sum of three sine curves is firstly reduced and then increased.
The grating efficiency distribution curve of the invention can be used for guiding the thickness change in the process of manufacturing the wedge-shaped holographic body grating, and can also be practically applied to the exposure process of the holographic body grating. The diffraction efficiency of the holographic body grating has close relation with the energy of the exposure light beam, and the exposure energy of the two light beams is regulated according to the grating efficiency distribution curve, so that the holographic body grating with the peak diffraction efficiency changing according to the curve can be obtained, the obtained light beam is uniform, and the imaging is uniform.
In addition, the grating efficiency distribution curve can provide thought for the partition of the grating, and the grating efficiency distribution curve can be selectively partitioned along the grating vector or in the direction perpendicular to the grating vector or in both directions. When the number of partitions is small, the peak efficiency in each region can be obtained by discretizing the formula (III), i.eDividing into a plurality of sections, and then carrying out the operation of the formula (III). When the number of partitions is large and the variation is nearly continuous, the formula (III) is required.
Examples
As shown in fig. 4, the positions of the incident grating 1, the intermediate grating 2, and the exit grating 3 are distributed in an "L" shape. The FOV of the input image source is 30 ° x 23 °, and the light rays in the whole field of view are traced by zemax optical design software, so that the illuminance distribution on the three gratings can be obtained as shown in fig. 4. And smoothing the trace result by using a mean algorithm to obtain more continuous point set distribution. For each grating, points in two directions parallel to the grating vector and perpendicular to the grating vector are selected to represent the illuminance distribution of the whole grating, and the specific selected directions are shown in fig. 4:
the first straight line 4 in the incident grating 1 coincides with the grating vector of the incident grating and passes through the center point of the incident grating, and the second straight line 5 is perpendicular to the incident grating vector and also passes through the center point of the incident grating. The third straight line 6 in the intermediate grating 2 coincides with the intermediate grating vector and passes through the highest illumination point of the intermediate grating, and the fourth straight line 7 is perpendicular to the intermediate grating vector and passes through the middle point of the third straight line 6. A fifth line 8 in the exit grating 3 coincides with the exit grating vector and passes the intersection of line 6 and the upper boundary of the intermediate grating, a sixth line 9 is perpendicular to the fifth line 8 and the fifth line 8 passes the midpoint of the sixth line 9. Fig. 5 shows the distribution of the points at the location of the third line 6 and fig. 6 shows the distribution of the points at the location of the sixth line 9.
The point set of six straight line positions is led into matlab, the least square method is used for fitting, the fitting model adopts two kinds of polynomials and sine curves, and as a result, the first straight line 4, the third straight line 6 and the fifth straight line 8 are found to meet the formula (I), and taking fig. 5 as an example, the curve equation is:
;
the second straight line 5, the fourth straight line 7 and the sixth straight line 9 are all fullFoot formula @) Taking fig. 6 as an example, the curve equation is:
the characterization method uniformly summarizes the illuminance distribution of three gratings in the holographic waveguide display system, and optical coupling elements with different peak diffraction efficiencies only need to multiply coefficients on the basis of an initial model, so that a precise ray tracing process with huge time consumption is not needed.
After the grating illuminance partition curve is determined, the illuminance distribution curve is integrated to obtain the total illuminance in the direction, the total illuminance is divided by the integration interval to obtain the average illuminance, the average illuminance is divided by the illuminance at each position, and the obtained value is multiplied by the initial grating efficiency at the position to obtain the new grating efficiency distribution curve. The method reduces high illumination and improves low illumination, thereby achieving the compensation effect. The overall calculation method can be summarized as the following formula:
(Ⅲ)：
wherein,for the grating efficiency profile +.>For the upper and lower limit of the integration position, +.>For peak efficiency of the initial grating +.>Is an illuminance distribution curve. Wherein it is noted that the diffraction efficiency +.>Edges of (2)The maximum diffraction efficiency was 100%. The grating efficiency distribution curves of the incident grating, the intermediate grating and the emergent grating in the grating vector direction obtained by the method have opposite trends with the illuminance distribution curve, and the decreasing trend of the formula (I) is met; the grating efficiency distribution curve in the direction perpendicular to the grating vector accords with the trend of the sum formula (II) of three sine curves, which is firstly reduced and then increased.
(Ⅰ)：
(Ⅱ)：
The characterization method provides a thought for grating partition, and can select to divide along the grating vector or perpendicular to the direction of the grating vector or divide the two directions simultaneously.
FIG. 7 shows a simpler partitioning method of equally dividing the intermediate grating into four sections along the direction of the grating vector, the peak efficiency in each section being determined by discretized equation (III), i.eDividing into a plurality of sections, and then carrying out the operation of the formula (III). The volume grating is divided into innumerable blocks along the direction of the grating vector by the special manufacturing process, so that the volume grating is continuously changed, and the formula (III) is obtained. Fig. 8 shows a comparison of the luminance distribution of the gratings before and after the partitioning, and it can be seen from the graph that the luminance uniformity of the entire luminance range is greatly improved.
The foregoing embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the present invention and to implement the same according to the present invention, not to limit the scope of the present invention. It will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (6)
1. A grating efficiency distribution characterization and optimization method for realizing uniform imaging of a holographic waveguide display system characterizes illuminance distribution of a grating in a two-dimensional pupil expansion structure of holographic waveguide display, and the grating comprises an incident grating (1), an intermediate grating (2) and an emergent grating (3); characterized in that the illuminance distribution curve f (t) in the grating vector direction in the incidence grating (1), the intermediate grating (2) and the exit grating (3) 1 ) The change trend of the fourth-order polynomial curve shown in the formula (I) is satisfied:
(I):f(t 1 )＝p 1 ·t 1 4 +p 2 ·t 1 3 +p 3 ·t 1 2 +p 4 ·t 1 +p 5
in p 1 、p 2 、p 3 、p 4 、p 5 Represents a fourth order polynomial curve f (t 1 ) Weighting coefficient t of (2) 1 Representing position coordinates in the direction of the grating vector;
the method comprises the following steps:
step 1: carrying out full-view field ray tracing on a two-dimensional pupil expansion structure displayed by the holographic waveguide;
step 2: obtaining an illuminance distribution two-dimensional graph on an incident grating (1), an intermediate grating (2) and an emergent grating (3) by using a detector element;
step 3: the main illuminance distribution of the grating is described by respectively taking points in two directions parallel to the grating vector and perpendicular to the grating vector in the incident grating (1), the intermediate grating (2) and the emergent grating (3); specific:
selecting a first straight line (4) and a second straight line (5) from the incident grating (1), wherein the first straight line (4) coincides with a grating vector of the incident grating and passes through a center point of the incident grating (1), and the second straight line (5) is perpendicular to the incident grating vector and passes through the center point of the incident grating (1);
selecting a third straight line (6) and a fourth straight line (7) from the intermediate grating (2), wherein the third straight line (6) coincides with the intermediate grating vector and passes through the highest illumination point of the intermediate grating (2), the fourth straight line (7) is perpendicular to the third straight line (6), and the fourth straight line (7) passes through the middle point of the third straight line (6);
selecting a fifth straight line (8) and a sixth straight line (9) from the emergent grating (3), wherein the fifth straight line (8) coincides with the emergent grating vector and passes through an intersection point of the third straight line (6) and the upper boundary of the intermediate grating (2), the sixth straight line (9) is perpendicular to the fifth straight line (8), and the fifth straight line (8) passes through the middle point of the sixth straight line (9);
step 4: and when the energy distribution on the grating is reversely deduced to be uniform, grating efficiency distribution curves which are required to be met by different positions on the grating are deduced to compensate energy loss caused by reflection of the light beam on the holographic body grating, so that the TOC and imaging are uniform.
2. The method for characterizing and optimizing the grating efficiency distribution for achieving uniform imaging of a holographic waveguide display system according to claim 1, wherein: the two-dimensional illuminance distribution of the incidence grating (1), the intermediate grating (2) and the emergent grating (3) is discrete, the two-dimensional illuminance distribution is smoothed by using a mean algorithm in a two-dimensional plane to obtain a continuously distributed point set, and the continuously distributed point set is fitted by using a least square method to obtain an illuminance distribution curve of the grating in two linear dimensions.
3. The method for characterizing and optimizing the grating efficiency distribution for achieving uniform imaging of a holographic waveguide display system according to claim 2, wherein: illuminance distribution curve f (t) in the direction perpendicular to the grating vector in the incidence grating (1), the intermediate grating (2) and the emission grating (3) 2 ) The trend of the sum of three sinusoids shown in the formula (II) is satisfied:
(II):f(t 2 )＝a 1 ·sin(b 1 t 2 +c 1 )+a 2 ·sin(b 2 t 2 +c 2 )+a 3 ·sin(b 3 t 2 +c 3 )
in which a is 1 、a 2 、a 3 Representing the illuminance distribution curve coefficients of the incident, intermediate and exit gratings, b 1 、b 2 、b 3 Respectively represent incidence, middle and exitThe illuminance of the jet grating meets the periodicity of the sine function distribution, c 1 、c 2 、c 3 Respectively representing the position relation of the illuminance distribution of the incidence grating, the middle grating and the emergent grating, t 2 Representing the position coordinates of the raster vector in the vertical direction.
4. The method for characterizing and optimizing the grating efficiency distribution for achieving uniform imaging of a holographic waveguide display system according to claim 2, wherein the grating efficiency distribution curve is obtained by:
integrating the illuminance distribution curves of the two dimensions of the grating to obtain total illuminance;
dividing the total illuminance by the integration interval to obtain average illuminance in the whole range;
dividing the average illumination by the illumination at each position, and multiplying the obtained value by the initial grating efficiency at the position to obtain a new grating efficiency distribution curve;
the calculation formula is as follows:
(Ⅲ)：
wherein eta (x) is a grating efficiency distribution curve, x 1 ，x 2 Is the upper and lower limit of the integral position, eta 0 Peak efficiency for the initial grating; f (x) is an illuminance distribution curve.
5. The method for characterizing and optimizing the grating efficiency distribution for achieving uniform imaging of a holographic waveguide display system according to claim 4, wherein:
the grating efficiency distribution curves of the incidence grating (1), the intermediate grating (2) and the emergent grating (3) in the grating vector direction have opposite trends with the illuminance distribution curve, and conform to the fourth-order polynomial decreasing trend; the grating efficiency distribution curve in the direction perpendicular to the grating vector accords with the trend that the sum of three sine curves is firstly reduced and then increased.
6. The method for characterizing and optimizing the grating efficiency distribution for achieving uniform imaging of a holographic waveguide display system according to claim 4, wherein: when dividing the grating based on the grating efficiency distribution curve, dividing along the grating vector or the direction perpendicular to the grating vector or dividing the grating in two directions simultaneously is selected.
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