Patent Description:
A surveying instrument typically comprises a base, an alidade rotatable about a first axis relative to the base, and an optical measuring instrument having a measuring axis rotatable about a second axis relative to the alidade. The base is used for mounting the instrument on the ground, a floor, a wall, or any other object and may include, for example, a tripod. The base defines the first axis about which the alidade is rotatable relative to the base. Typically, the base is mounted such that the first axis is orientated in the vertical direction. The alidade defines the second axis about which the optical measuring instrument is rotatable relative to the alidade. Typically, the first and second axes are orthogonal to each other. The optical instrument defines the measuring axis which is an axis of the measuring instrument along which a measurement can be performed using the optical instrument. For example, the optical measuring instrument can be of a type emitting a laser beam along the measuring axis and detecting laser light of the beam reflected from an object in order to determine the distance between the object and the optical measuring instrument. The measuring axis and the second axis are typically orientated orthogonal to each other.

The measuring instrument may comprise rotational encoders measuring the rotational positions of the alidade about the first axis relative to the base and of the optical measuring instrument about the second axis relative to the alidade. It is then possible to determine the orientation of the measuring axis in a coordinate system defined relative to the base such that the measurement performed along the measuring axis can be associated with this coordinate system.

The orientation of the measuring axis in the coordinate system can be determined by a calculation using the orientation of the first axis in the coordinate system, the measured orientation of the alidade about the first axis relative to the base and the measured orientation of the measuring instrument about the second axis relative to the alidade as inputs. The calculation further depends on the angle between the first axis and the second axis and the angle between the second axis and the measuring axis. These angles are defined by the mechanical structure of the surveying instrument, and surveying instruments are typically designed such that these angles amount to <NUM>°. However, these angles deviate from the angles which are expected according to the design of the instrument due to mechanical imperfections, and these angles may change over time due to influences from the environment, such as changing temperatures.

There are known methods of calibrating a surveying instrument in which the angles mentioned above, or the deviations of these angles from the angles expected based on the design of the surveying instrument, can be measured using a dedicated measuring setups external to the surveying instrument. Typically, such calibration methods are performed in a factory, a site operated by a supplier of the measuring instrument, or a site of a user of the measuring instrument, provided that he has the necessary additional tools available. These methods may provide an accurate calibration but consume significant amounts of time and/or resources since the instrument must be brought to the site where the calibration can be done or the necessary tools must be purchased. Moreover, these methods do not provide estimates of temporal changes of the errors occurring in the field during a surveying excursion subsequent to a most recent calibration.

Therefore, it is desirable to provide a method of calibrating a surveying instrument and a surveying instrument facilitate the calibration of the surveying instrument.

<CIT> discloses a device having a scan function comprising an electro-optical distance measuring element having a laser axis as the target axis, a motorized optical deflection unit, which deflects the target axis by a deflection angle, and an angle measuring element for determining at least one angular position of the deflection unit. A first measurement of angle coordinates of a reticle in a first angular position of the deflection unit as the first position, and a second measurement of angle coordinates of the reticle in a second angular position of the deflection unit as the second position are performed. The first and second measurements of the reticle are carried out on the basis of images taken with a camera, the optical axis of which is deflected by the deflection unit, and calibration parameters are determined on the basis of the angular positions and the angular coordinates in the first and second positions.

The present invention has been accomplished taking the above considerations into account.

Thus, it is an object of the present invention to provide an improved method of calibrating a surveying instrument, and to provide an improved surveying instrument capable of performing a method of calibration.

Embodiments of the present invention provide methods for calibrating a surveying instrument which comprises a base, an alidade rotatable about a first axis relative to the base, and an optical measuring instrument having a measuring axis rotatable about a second axis relative to the alidade. The first and second axes can be substantially orthogonal to each other, but this is not required. Similarly, the measuring axis and the second axis can be substantially orthogonal to each other, but this is also not required.

The surveying instrument can be a surveying instrument of any type having a measuring axis. Examples of such surveying instruments include those known as a theodolite, a tachymeter, a total station, a scanner, a laser range finder and a dumpy level in the art, for example.

According to exemplary embodiments, the surveying instrument is configured such that a beam path for a light beam is provided using components such as, for example, a light source for emitting the light beam, zero or more lenses for collimating the light beam, zero or more mirrors for folding the beam path, zero or more beam splitters and a position sensitive detector for detecting light of the light beam. The light source can be fixed to the base, the alidade or the optical measuring instrument. The detector can be fixed to the base, the alidade or the optical measuring instrument. The beam path extends between one of the components fixed to the base and one of the components fixed to the optical measuring instrument. This portion of the beam path can be provided such that the light beam extends between the one component and the other component directly, without traversing any further component, such as a lens, a beam splitter and a mirror, or this portion of the beam path may traverse further components, such as lenses, beam splitters and mirrors which influence the light beam traveling along the beam path by focusing, splitting, and folding, respectively.

The provided beam path between the light source and the detector includes the portion extending between the component fixed to the base and the component fixed to the measuring instrument, and it may include further portions upstream or downstream of this particular portion. Again, these further portions of the beam path can be defined using other components, such as lenses, beam splitters and mirrors, mounted on the base, the alidade and the optical measuring instrument.

According to further exemplary embodiments, the surveying instrument is configured such that the beam path between the one component fixed to the base and the other component fixed to the optical measuring instrument exists for at least a first range of rotational positions of the optical measuring instrument about the second axis. This means that it is not required that the beam path exists for all possible orientations of the optical measuring instrument about the second axis.

According to exemplary embodiments herein, the beam path further exists for a second range of rotational positions of the optical measuring instrument about the second axis, wherein the second range is different from the first range. For example, the orientation of the measuring instrument relative to alidade has to be changed by more than π/<NUM> or π/<NUM> between a first orientation in which the measuring instrument is orientated at the center of the first range and a second orientation at which the measuring instrument is orientated at the center of the second range. In such embodiments, the beam path is not required to exist for orientations other than orientations within the first and second ranges. However, the beam path may also exist for other orientations outside the first and second ranges.

According to further embodiments, the beam path exists for at least two or at least three different ranges of orientations of the alidade relative to the base about the first axis. Again, centers of the these two or three or more different ranges of orientations may differ by more than π/<NUM> or more than π/<NUM>.

According to exemplary embodiments, a method of calibrating a surveying instrument comprises using a surveying instrument comprising a base, an alidade rotatable about a first axis relative to the base, and an optical measuring instrument having a measuring axis rotatable about a second axis relative to the alidade, and performing plural measurements, wherein each measurement includes detecting, using the detector, light of the light beam traveling from the light source along the beam path to the detector when the alidade is in a given rotational position about the first axis and the optical instrument is in a given rotational position about the second axis.

According to exemplary embodiments, at least one error of the surveying instrument is determined based on the plural measurements. The at least one error of the surveying instrument represents a deviation of an actual property of the surveying instrument from a corresponding expected property of the surveying instrument.

According to some embodiments, the determined at least one error includes a deviation of the angle between the first axis and the second axis from the expected angle between the first axis and the second axis. This error is referred to as the trunnion axis error in the art.

According to further exemplary embodiments, the at least one error includes a deviation of an angle between the measuring axis and the second axis and an expected angle between the measuring axis and the second axis. This error is referred to as collimation error in the art.

According to further exemplary embodiments the at least one error includes a difference between the orientation which is orthogonal to the first axis and the orientation of the measuring axis when it is expected to be orientated orthogonal to the first axis. This error is referred to as vertical index error in the art.

According to further exemplary embodiments, the surveying instrument comprises a base; an alidade rotatable about a first axis relative to the base; and an optical measuring instrument rotatable about a second axis relative to the alidade; wherein the optical measuring instrument is configured to emit a beam of measuring light along a measuring axis of the optical measuring instrument; wherein the optical measuring instrument comprises a position-sensitive detector and optics to image a distant object onto the detector; wherein the surveying instrument comprises a mirror fixed to the base; and wherein the optical measuring instrument can be oriented such that the beam of measuring light is reflected from the mirror fixed to the base such that it is incident on the detector of the optical measuring instrument.

According to further exemplary embodiments, a method of calibrating such surveying instrument comprises performing plural measurements at different rotational positions of the alidade about the first axis and plural rotational positions of the optical measuring instrument about the second axis, wherein, in each of the plural measurements, the optical measuring instrument is oriented such that the beam of measuring light is reflected from a mirror fixed to the base and incident on the detector; and determining at least one property of a coordinate transformation between a coordinate system of the detector and a coordinate system of the surveying instrument based on the plural measurements.

According to some particular embodiments, the at least one property of the coordinate transformation between a coordinate system of the detector and the coordinate system of the surveying instrument includes data representing a position on the detector onto which a location of the distant object is imaged where the measuring light beam is incident on the distant object.

When the surveying instrument is used, the optical measuring instrument is oriented such that the measuring light beam points to a desired location on the distant object, and the measuring light beam can be used to perform a measurement, such as to determine the distance of the selected location from the surveying instrument. In order to orient the optical measuring instrument such that such that the measuring light beam points to the desired location of the distant object, the image of the object recorded using the detector can be monitored. The image may include a representation of a reticle or similar element indicating the position in the image corresponding to the location on the distant object onto which the measuring light beam is directed. For this purpose, it is desirable that the position in the image indicated by the reticle exactly corresponds to the location on the distant object onto which the measuring light beam is directed. The above method can be helpful to establish this correspondence. In particular, the method allows to determine a pixel of the detector onto which the location of the distant object is imaged onto which the beam of measuring light is directed. This pixel is also referred to as the center pixel of the detector in the art.

The forgoing as well as other advantageous features of this disclosure will be more apparent from the following detailed description of exemplary embodiments with reference to the accompanying drawings, in which:.

In the exemplary embodiments described below, components that are alike in function and structure are designated as far as possible by like reference numerals. Therefore, to understand the features of the individual components of a specific embodiment, the descriptions of other embodiments and of the summary of the invention should be referred to.

<FIG> are schematic illustrations of an exemplary surveying instrument wherein each figure illustrates a certain type of axis error of the surveying instrument <NUM>. The surveying instrument <NUM> is a theodolite in the illustrated example. The surveying instrument <NUM> comprises a base <NUM> which includes a tripod <NUM>, and an alidade <NUM> which is rotatable relative to the base <NUM> about a first axis <NUM>. In most surveying scenarios, it is desired that the first axis <NUM> is orientated vertically and the tripod <NUM> is used to adjust the orientation of the base <NUM> such that the first axis <NUM> is parallel to the vertical direction defined by the gravity vector at the location of the instrument <NUM>. The surveying instrument <NUM> further comprises an optical measuring instrument <NUM> which is mounted on the alidade <NUM> such that it is rotatable relative to the alidade <NUM> about a second axis <NUM>. The illustrated surveying instrument is designed such that the second axis <NUM> is orientated orthogonally to the first axis <NUM>. The measuring instrument includes optics <NUM>, such as a telescope, defining a measuring axis <NUM> along which a measurement can be performed using the optical measuring instrument <NUM>. For example, the measuring axis <NUM> can be indicated by a reticle in the visual field of the telescope, and the user can direct the measuring axis <NUM> to an object of interest in the visual field of the telescope by rotating the measuring instrument <NUM> about the second axis <NUM> and the alidade <NUM> about the first axis <NUM>. The user can then determine the orientations about the first and second axes <NUM>, <NUM> by reading scales provided on the instrument or electronic signals generated by encoders associated with the first and second axes <NUM>, <NUM> in the surveying instrument <NUM>. Based on these readings, an angular position of the object of interest can be determined relative to a coordinate system associated with the base <NUM>. The calculation of this orientation depends on the readings of the rotational positions about the first and second axes <NUM>, <NUM> as inputs. The calculation further depends on assumptions on the geometry of the surveying instrument <NUM>. The assumptions on the geometry include the orientations of the first axis, the second axis and the measuring axis relative to each other. If the configuration of the surveying instrument <NUM> deviates from these assumptions, this will result in an inaccurate calculation of the orientation of the measuring axis in the coordinate system.

<FIG> illustrates one type of such error, known as the vertical index error in the art. The vertical index error is indicative of an angle <NUM> between a line <NUM> which is exactly orthogonal to the first axis <NUM> and the measuring axis <NUM> when the measuring instrument <NUM> is orientated relative to the alidade <NUM> such that the angle between the first axis <NUM> and the measuring axis <NUM> should be <NUM>° according to a scale provided on the instrument or the readings of the encoder associated with the rotation of the measuring instrument <NUM> about the second axis <NUM>, assuming that the reading of the encoder or scale is at <NUM>° when the measuring instrument is orientated such the measuring axis <NUM> is orientated upwards, pointing to the zenith.

<FIG> illustrates a type of error which is known as the collimation error in the art. This error is indicative of an angle <NUM> between an axis <NUM> which is orthogonal to the second axis <NUM> and the measuring axis <NUM>.

<FIG> illustrates a type of error known as the trunnion axis error in the art. This error is indicative of an angle <NUM> between the second axis <NUM> and a direction <NUM> which is exactly orthogonal to the first axis <NUM>.

<FIG> illustrates an error known as the tilting axis error in the art, which is indicative of an angle <NUM> between the second axis <NUM> and the vertical direction <NUM> as defined by gravity at the location of the instrument <NUM>.

The tilting axis error is a set-up error introduced by the user when mounting the instrument <NUM> and cannot be eliminated by a calibration of the instrument itself. The other three errors, the vertical index error, the collimation error, and the trunnion axis error depend only on the configuration of the surveying instrument <NUM> itself and are errors intrinsic to the instrument. The embodiments of calibration methods illustrated below seek to determine these or other types of errors of a surveying instrument.

<FIG> is a schematic illustration of a surveying instrument <NUM>. The surveying instrument <NUM> comprises a base <NUM> and an alidade <NUM> which is mounted on the base <NUM> such that it is rotatable relative to the base <NUM> about a first axis <NUM>. The surveying instrument <NUM> further comprises an optical measuring instrument <NUM> which is mounted on the alidade <NUM> such that it is rotatable about a second axis <NUM> relative to the alidade <NUM>. The second axis <NUM> is substantially orthogonal to the first axis <NUM>. The measuring instrument <NUM> includes optics, such as a telescope, which is schematically represented by a front lens <NUM> in <FIG>. The optics mounted on the measuring instrument defines a measuring axis <NUM> which is substantially orthogonal to the second axis <NUM>. In the illustration of <FIG>, the measuring instrument <NUM> is further orientated about the second axis <NUM> relative to the alidade <NUM> such that the measuring axis <NUM> is orthogonal to the first axis <NUM> and the plane of the drawing.

The surveying instrument <NUM> further comprises a calibration system <NUM> which can be used to determine properties of the surveying instrument <NUM>. These properties may in particular include information on the relative orientations of the first axis <NUM>, the second axis <NUM> and the measuring axis <NUM>.

The calibration system <NUM> comprises optical components providing a beam path between a light source <NUM> and a detector <NUM>. The optical components may include, apart from the light source <NUM> and the detector <NUM>, lenses, mirrors and beam splitters or other suitable optical components which can be used to provide a suitable beam path between the light source <NUM> and the detector <NUM>. In the embodiment illustrated in <FIG>, the light emitted from the light source <NUM> traverses a pinhole <NUM> including a plate having a small opening such that a divergent beam of light is formed downstream of the pinhole <NUM>. This beam is collimated by a lens <NUM>.

It is to be noted that other components, such as a light emitting diode (LED), can be used to produce the divergent beam of light instead of the shown combination of the light source <NUM> and the pin hole <NUM>.

Moreover, the calibration system <NUM> comprises an actuator <NUM> controlled by the controller <NUM> and configured to displace the collimating lens <NUM> in a direction of its optical axis as indicated by arrow <NUM> in <FIG>. The actuator <NUM> can be controlled in order to adjust the collimation of the beam generated from light source <NUM> and to adjust a focus generated on the detector <NUM> from an incoming beam.

The light beam is subsequently incident on a beam splitter <NUM> from which a portion of the light beam is reflected. The portion of the light beam reflected from the beam splitter <NUM> is incident on a beam splitter <NUM> having a mirror surface <NUM> reflecting the light beam. The mirror surface <NUM> is positioned such that the first axis <NUM> intersects the mirror surface <NUM>, and it is orientated such that the light beam reflected from the mirror surface <NUM> travels in a direction substantially parallel to the first axis <NUM>. The light beam reflected from the mirror surface <NUM> traverses the alidade <NUM> and is incident on a mirror surface <NUM> provided on a mirror <NUM>. For example, the mirror <NUM> can be provided by a glass plate having two parallel main surfaces, wherein one surface carries a metal layer. The metal layer has two opposite reflective surfaces <NUM> and <NUM>' wherein light beam is reflected from the reflective surface <NUM> in the situation shown in <FIG>. The mirror <NUM> is fixed to the measuring instrument <NUM> such that it has a fixed mechanical position and orientation relative to the measuring axis <NUM>.

The light of the light beam incident on the mirror <NUM> and reflected from the mirror surface <NUM> travels back to the beam splitter <NUM> where it is reflected from the mirror surface <NUM> such that it is directed to the beam splitter <NUM>, traversing the collimation lens <NUM>. A portion of this light traverses the beam splitter <NUM> without being reflected such that it is incident on the detector <NUM>. The detector <NUM> is arranged at a same distance from the collimation lens <NUM> as the pin hole <NUM> such that the beam is substantially focused on the detector <NUM>.

The illustrated beam path of the light beam from the light source <NUM> to the detector <NUM> comprises plural portions: a portion between the light source <NUM> and the beam splitter <NUM>, a portion extending from the beam splitter <NUM> to the beam splitter <NUM> mounted on the base <NUM>, a portion extending from the beam splitter <NUM> to the mirror <NUM> mounted on the optical measuring instrument <NUM>, a portion extending from the mirror <NUM> mounted on the measuring instrument <NUM> to the beam splitter <NUM> mounted on the base <NUM>, a portion extending from the beam splitter <NUM> to the beam splitter <NUM>, and a portion extending from the beam splitter <NUM> to the detector <NUM>.

The detector <NUM> is a position sensitive detector such that a position at which the light beam is focused on the detector <NUM> can be determined from signals generated by the detector <NUM>. According to some embodiments, the detector <NUM> comprises an array of detector pixels wherein each detector pixel provides a light detector. The position of the incident light beam on the detector can be determined from detection signals generated by the array of detector pixels. For example, the light beam can be simultaneously incident on plural detector pixels. The determination of the position of the light beam on the detector may include a determination of a center of gravity of the light intensity incident on the detector <NUM> and detected by the detector <NUM>. The surveying instrument <NUM> may include a controller <NUM> including a calculator, such as a microcomputer, analyzing the detection signals generated by the detector and generating light position data representing the position on the detector <NUM> where the light beam is incident on the detector <NUM>. The light position data can be generated based on the center of gravity of the detected light intensity as illustrated above.

The beam path having at least one portion extending between a component mounted on the base <NUM>, which is the beam splitter <NUM> in the illustrated example, and a component mounted on the measuring instrument <NUM>, which is the mirror <NUM> in the illustrated example, exists for plural rotational positions of the measuring instrument <NUM> relative to the alidade <NUM> about the second axis <NUM>, and for plural rotational positions of the alidade <NUM> relative to the base <NUM> about the first axis <NUM>.

In practice, the surface of the mirror <NUM> is not perfectly orthogonal to the first axis <NUM>, and the light beam incident on the mirror <NUM> is not perfectly aligned with the first axis <NUM>. Therefore, the positions of incidence of the light beam on the detector <NUM> will be arranged on a circle when the alidade <NUM> is rotated about the first axis <NUM>.

Moreover, when the optical measuring instrument <NUM> is rotated about the second axis <NUM>, the positions of incidence of the light beam on the detector <NUM> will be arranged on a substantially straight line on the detector <NUM>.

<FIG> is an illustration of measuring results obtained with the calibration system <NUM> of the surveying instrument shown in <FIG>. The performing of one measurement includes orienting the alidade <NUM> to a given rotational position about the first axis <NUM>, orienting the measuring instrument <NUM> to a given rotational position relative to the alidade <NUM> about the second axis <NUM>, reading a detected image from the detector <NUM>, determining the position of the incident light beam within the read image, and recording the light position data corresponding to the determined position. Thus, one measurement is characterized by two rotational positions and the light position data associated with these two rotational positions.

The two rotational positions can be represented as a pair in which the first element indicates the given rotational position of the alidade <NUM> about the first axis <NUM>, and the second element indicates the given rotational position of the measuring instrument <NUM> about the second axis <NUM>.

The measurement results illustrated in <FIG> are arranged in groups or sets of measurements, wherein each set includes measurements performed at the same given rotational positions of the alidade <NUM> about the first axis <NUM> but different rotational positions of the measuring instrument <NUM> about the second axis <NUM> and, similarly, sets including measurements performed at different rotational positions of the alidade <NUM> about the first axis <NUM> but the same rotational positions of the measuring instrument <NUM> about the second axis <NUM>.

<FIG> shows location data representing locations of incidence of the light beam on the detector <NUM> in a two-dimensional coordinate system. In the illustrated embodiment, the coordinate system is selected such that the abscissa indicates pixel locations in an x-direction of the detector <NUM>, and the ordinate indicates pixel locations in a y-direction of the detector <NUM>. Symbols having shapes of a rectangle, a triangle, a cross and a star indicate measured positions of the light beam on the detector <NUM> at given rotational positions. The measurements are each labeled by a pair of numbers wherein the first number indicates the rotational position of the alidade <NUM> about the first axis <NUM> and the second number indicates the rotational position of the measuring instrument <NUM> about the second axis <NUM>.

<FIG> shows a set of sixteen measurements performed at four different rotational positions of the alidade <NUM> about the first axis <NUM> and four different positions of the measuring instrument <NUM> about the second axis <NUM>. It is apparent from <FIG> that the light positions of measurements performed at the same given rotational position of the alidade <NUM> about the first axis <NUM>, but different rotational positions of the measuring instrument <NUM> about the second axis <NUM>, are substantially arranged along straight lines <NUM> in the coordinate system of the detector <NUM>. It is further apparent from <FIG> that the light positions on the detector <NUM> of measurements performed at different given rotational positions of the alidade <NUM> about the first axis <NUM> but the same rotational position of the measuring instrument <NUM> about the second axis <NUM> are substantially arranged on concentric circles <NUM> having a same center <NUM>.

It is apparent from <FIG>, that a change of the rotational position of the measuring instrument <NUM> about the second axis <NUM> from a rotational position corresponding to an encoder reading of <NUM> gon at measurement (<NUM>,<NUM>) to a rotational position corresponding to an encoder reading of <NUM> gon at measurement (<NUM>,<NUM>) results in a smaller circle <NUM>. Similarly, a change of the rotational position of the measuring instrument <NUM> about the second axis <NUM> from the measurement (<NUM>,<NUM>) to a rotational position corresponding to an encoder reading of <NUM> gon at measurement (<NUM>,<NUM>) results again in a smaller circle. However, a similar change of the rotational position of the measuring instrument <NUM> about the second axis <NUM> from measurement (<NUM>,<NUM>) to a rotational position corresponding to an encoder reading of <NUM> gon at measurement (<NUM>,<NUM>) results in a circle <NUM> of a greater diameter. This means that there exists a smallest achievable circle <NUM> at a rotational position of the measuring instrument <NUM> about the second axis <NUM> somewhere between the encoder readings of <NUM> gon and <NUM> gon. This position is indicated by reference numeral <NUM> in <FIG>. The line <NUM> is a tangent to this smallest circle <NUM> having a radius r1. A straight line through the center <NUM> and the position <NUM> is orthogonal to the line <NUM>. Positions on the line <NUM> can be represented using the encoder readings as a parameter.

The rotational position of the measuring instrument <NUM> about the second axis <NUM> corresponding to this position <NUM> can be obtained by fitting a straight line to the light positions determined in a set of measurements ((<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); or (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>) in <FIG>) performed at the same rotational positions of the alidade <NUM> about the first axis <NUM> and different rotational positions of the measuring instrument <NUM> about the second axis <NUM>. The position <NUM> can then be determined by finding that position on the determined line <NUM> which comes closest to the common center <NUM> of the circles <NUM>. The center <NUM> can be determined by fitting a circle to light positions of each set of measurements of the plural sets of measurements ((<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>); and (<NUM>,<NUM>), (<NUM>,<NUM>), (<NUM>,<NUM>) and (<NUM>,<NUM>) in <FIG>) performed at different given rotational positions of the alidade <NUM> about the first axis <NUM> and same given rotational positions of the measuring instrument <NUM> about the second axis <NUM>.

In the illustrated example, the center of each circle is determined by fitting a circle to the light positions of four measurements. However, the number of measured light positions can be three or greater than four. Moreover, the center of a circle can be determined based on two measured light positions if the surveying instrument includes a sufficiently accurate angle measuring instrument to measure the orientation of the alidade <NUM> relative to the base <NUM> about the first axis <NUM>. A first measurement can be performed at a first orientation of the alidade <NUM> relative to the base <NUM>. Thereafter, the alidade <NUM> is rotated about the first axis <NUM> by <NUM>° as measured by the angle measuring instrument, and a second measurement is performed in this position. The center of the circle is located half-way between the light positions of the first and second measurements.

While the radius r1 can be determined as the distance between the center <NUM> of the circles <NUM> and the closest point <NUM>, it is also possible to calculate the radius r1 of the smallest circle <NUM> by determining the distance between the straight line <NUM> fitted to the light positions of measurements (<NUM>,<NUM>),. (<NUM>,<NUM>) and the straight line <NUM> fitted to the light positions of the measurements (<NUM>,<NUM>),. (<NUM>,<NUM>). In order to determine the position of the circle center <NUM>, a set of measurements is required which includes a set of at least two measurements performed at the same given rotational position of the optical measuring instrument <NUM> about the second axis <NUM> but different given rotational positions of the alidade <NUM> about the first axis <NUM>. In order to determine a straight line <NUM> and the position <NUM> closest to the center <NUM>, a set of measurements comprising at least two measurements performed at the same given rotational positions of the alidade <NUM> about the first axis <NUM> but different given rotational positions of the optical measuring instrument <NUM> about the second axis <NUM>.

The smallest radius r1 and the rotational position of the measuring instrument <NUM> about the second axis <NUM> corresponding to the closest position <NUM> on line <NUM> can be used to determine at least one error of the surveying instrument <NUM> as will be illustrated further below.

<FIG> shows the surveying instrument <NUM> of <FIG> wherein, compared to <FIG>, the optical measuring instrument <NUM> has been rotated relative to the alidade about the second axis <NUM> by an angle of about <NUM>° corresponding to <NUM> gon. The surveying instrument <NUM> is configured such that the beam path of the calibration system <NUM> between the light source <NUM> and the detector <NUM> exists also for a range of rotational positions around this rotational position of the optical measuring instrument <NUM> about the second axis <NUM>. This can be achieved, for example, by providing the optical measuring instrument <NUM> with openings in its casing and its remaining components such that a through hole is formed in which the mirror <NUM> is arranged such that the light beam can be incident on the reflective surfaces <NUM> and <NUM>' of the mirror <NUM> from opposite sides. In the situation shown in <FIG>, the light beam is reflected from the reflective surface <NUM>' while it is reflected from the other reflective surface <NUM> in the situation shown in <FIG>. Herein, the mirror <NUM> is advantageously arranged on the optical measuring instrument <NUM> such that it does not interfere with the function provided by the optical measuring instrument <NUM>. For example, the mirror <NUM> can be arranged outside of the beam path of the telescope <NUM> of the measuring instrument <NUM>. Moreover, it is possible to provide the reflective surfaces <NUM> and <NUM>' on separate carriers rather than on a same side of a same plate.

This beam path also traverses components of the alidade <NUM> and the base <NUM>. This can be achieved, for example, by providing rotational bearings and a shaft connecting the alidade <NUM> to the base <NUM> with through holes extending in the axial direction and traversed by the beam path of the light beam. Such bearings and shafts are not illustrated in the figures for simplicity reasons.

A set of sixteen measurements is performed using the calibration system <NUM> also for this configuration of its beam path. The sixteen measurements are performed for four different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> and four different rotational positions of the alidade <NUM> about the first axis <NUM>. The positions of incidence of the light beam on the detector <NUM> obtained from these measurements are illustrated in <FIG> showing these positions in the coordinate system of the detector <NUM> corresponding to <FIG>.

It is apparent from <FIG> that light positions obtained from measurements performed at the same rotational positions of the alidade <NUM> about the first axis <NUM> but different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> are also arranged on straight lines <NUM> shown in <FIG>, similar to <FIG>. Moreover, light positions obtained from measurements performed at different orientations of the alidade <NUM> about the first axis <NUM> but the same orientations of the optical instrument <NUM> about the second axis <NUM> are arranged on circles having a common center <NUM>, similar to <FIG>.

It is now possible to determine the smallest possible circle (<NUM> in <FIG>) and the rotational position of the optical measuring instrument <NUM> about the second axis <NUM> were the straight lines <NUM> are closest to the center <NUM> (corresponding to position <NUM> in <FIG>) also for the position data shown in <FIG> and obtained with the configuration of the beam path of the calibration system <NUM> as shown in <FIG>.

It is apparent from <FIG> that the minimal circle arranged between pairs of parallel lines <NUM> about the center <NUM> has a radius r2 which is much smaller than the radius r1 derived from the measuring results shown in <FIG>.

This difference between the radii r1 and r2 can be explained as follows: In a surveying instrument <NUM> having an ideal configuration in which the second axis <NUM> is exactly orthogonal to the first axis <NUM> and in which the flat mirror surface <NUM> is exactly parallel to the second axis <NUM>, the radius of the minimal circle <NUM> can be zero because the optical measuring instrument <NUM> can be rotated about the second axis <NUM> to a rotational position in which the portion of the beam path extending between the beam splitter <NUM> fixed to the base <NUM> and the mirror <NUM> fixed to the optical measuring instrument <NUM> and the portion of the beam path extending between the mirror <NUM> and the beam splitter <NUM> are both exactly parallel to the first axis <NUM>. The beam is then incident on the detector at a position corresponding to the center <NUM> of all circles.

In practice, the surveying instrument <NUM> differs from this ideal configuration in that the second axis <NUM> is not exactly orthogonal to the first axis <NUM> and in that the flat mirror surface <NUM> is not exactly parallel to the second axis <NUM>. Both deviations contribute to the minimum radii r1 and r2 of the circles <NUM> illustrated above. The first deviation, which is the deviation of the angle between the first and second axes <NUM> and <NUM>, respectively, from <NUM>°, is the trunnion axis error k of the surveying instrument <NUM>. The second deviation, which is the deviation of the orientation of the mirror surface <NUM> from parallel to the second axis <NUM>, can be referred to as a "collimation error" cx of the mirror <NUM>.

Since the orientation of the mirror <NUM> has been changed by substantially <NUM>° between the configurations shown in <FIG> and <FIG> and since the mirror <NUM> is fixed to the measuring instrument <NUM>, the contribution of the deviation of the orientation of the mirror surface <NUM> to the radii r1 and r2 of the minimal circles <NUM> has a same absolute value but opposite signs for the two configurations shown in <FIG> and <FIG>. On the other hand, the contribution of the deviation of the angle between the first and second axes <NUM> and <NUM> from orthogonal is the same in both configurations.

Two minimal radii r1 and r2 can be determined from the two sets of measurements obtained at the two different rotational configurations of the optical measuring instrument <NUM> about the second axis <NUM>. The radii r1 and r2 can be expressed as follows: <MAT> <MAT>.

The two radii r1 and r2 can be used to calculate the two unknowns which are the trunnion axis error k of the surveying instrument <NUM> and the collimation error cx of the mirror <NUM> as follows: <MAT> <MAT>.

The values r1, r2, k and cx in formulas (<NUM>) to (<NUM>) can be determined in length units, such as millimeters or number of pixels on the detector. The values of k and cx can be translated to angular values better representing the trunnion axis error and the collimation error when the correspondence between positions on the detector and rotational positions about the first and second axes is known. This correspondence can be determined by a suitable calibration of rotational sensors associated with the first axis <NUM> and the second axis <NUM>, for example.

While the collimation error cx of the mirror <NUM> is of no relevance for the performance of the surveying instrument, the trunnion axis error k determined based on the two sets of measurements illustrated above is important information relating to the performance of the surveying instrument <NUM> and can be used to correct measurements performed using the surveying instrument <NUM>.

<FIG> shows the surveying instrument <NUM> shown in <FIG> and <FIG> in a third configuration. Specifically, the optical measuring instrument <NUM> shown in <FIG> is in a third orientation relative to the alidade <NUM> about the second axis <NUM> which is different from the orientations shown in <FIG> and <FIG>. In this orientation, the measuring axis <NUM> is orientated substantially parallel to the first axis <NUM>.

<FIG> shows further details of the optical measuring instrument <NUM>. Specifically, the optical measuring instrument <NUM> comprises a measuring light source <NUM> emitting a measuring light beam which traverses a beam splitter <NUM> and is collimated and further shaped by optics not shown in <FIG>. The measuring light beam is emitted from the optical measuring instrument <NUM> through a front lens <NUM>. In a surveying situation, the light beam emitted from the optical measuring instrument <NUM> is directed to an object of interest, and light reflected back from the object of interest is received through the front lens <NUM> and directed onto a detector <NUM> by the beam splitter <NUM>. The detector can be of a type suitable for performing the function of the surveying instrument <NUM>. For example, the detector <NUM> can be configured to determine a time when a light pulse is received back from the object of interest to determine the distance of the object of interest from the measuring instrument <NUM> if the surveying instrument <NUM> is an electronic distance meter, or the detector <NUM> can be a position sensitive detector if the surveying instrument <NUM> is a total station.

The mirror <NUM> arranged in the beam path of the calibration system <NUM> in <FIG> and <FIG> does not interfere with the measuring beam path of the optical measuring instrument <NUM>.

The light source <NUM> of the optical measuring instrument <NUM> is also a part of the calibration system <NUM> in the configuration shown in <FIG>. Specifically, light of the measuring light source <NUM> is detected by the detector <NUM>. For this purpose a beam path exists between the light source <NUM> and the detector <NUM>. This beam path comprises a portion extending from the measuring light source <NUM> which is fixed to the optical measuring instrument <NUM>, to the beam splitter <NUM> which is fixed to the base <NUM>, and a portion extending from the beam splitter <NUM> to the detector <NUM>.

A set of sixteen measurements is performed using the calibration system <NUM> in the configuration shown in <FIG>. Again, the sixteen measurements are performed at four different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> and four different rotational positions of the alidade <NUM> about the first axis <NUM>. The positions of incidence of the light beam on the detector <NUM> obtained from these measurements are illustrated in <FIG> showing these positions in the coordinate system of the detector <NUM> corresponding to <FIG> and <FIG>. It is apparent from <FIG> that light positions obtained from measurements performed at the same given rotational positions of the alidade <NUM> about the first axis <NUM> but different given rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> are also arranged on straight lines <NUM> shown in <FIG>, similar to <FIG> and <FIG>. Moreover, light positions obtained from measurements performed at different orientations of the alidade <NUM> about the first axis <NUM> but the same orientations of the optical instrument <NUM> about the second axis <NUM> are arranged on circles having a common center <NUM>, also similar to <FIG> and <FIG>.

It is again possible to determine the smallest possible circle and the rotational position of the optical measuring instrument <NUM> about the second axis <NUM> were the straight lines <NUM> are closest to the center <NUM> (corresponding to position <NUM> in <FIG>) for the position data shown in <FIG> and obtained with the configuration of the beam path of the calibration system <NUM> as shown in <FIG>.

It is apparent from <FIG> that the minimal circle arranged between pairs of parallel lines <NUM> about the center <NUM> has a radius r3 which is different from the radii r1 and r2 obtained previously.

The radius r3 is greater than zero because of deviations of the surveying instrument <NUM> from its ideal configuration. These deviations mainly include the deviation of the angle between the first and second axes <NUM> and <NUM>, respectively, from <NUM>°, which is the trunnion axis error k of the surveying instrument <NUM>, and the deviation of the orientation of the measuring axis <NUM> from the direction orthogonal to the second axis <NUM>, which is the collimation error c of the surveying instrument <NUM>. Both of these deviations contribute to the radius r3 of the minimal circle, which can be written as <MAT>.

The trunnion axis error k of the surveying instrument <NUM> has been determined using formula (<NUM>) above based on the sets of measurements shown in <FIG> and <FIG>, so that the collimation error c of the surveying instrument <NUM> can be determined by <MAT>.

Both the collimation error c of the surveying instrument <NUM> and the trunnion axis error k are important information relating to the performance of the surveying instrument <NUM> and can be used to correct measurements performed using the surveying instrument <NUM>.

<FIG> schematically illustrates a surveying instrument <NUM> according to a second embodiment comprising a calibration system <NUM> which can be used to determine some errors of the surveying instrument <NUM>. The surveying instrument <NUM> shown in <FIG> is similar to the surveying instrument illustrated with reference to <FIG> in that it comprises a base <NUM>, an alidade <NUM> rotatable relative to the base <NUM> about a first axis <NUM>, and an optical measuring instrument <NUM> rotatable relative to the alidade <NUM> about a second axis <NUM>. The surveying instrument <NUM> is also configured to provide a calibration beam path between a light source <NUM> and a detector <NUM> for two different ranges of rotational positions of the optical measuring instrument <NUM> about the second axis <NUM>. The surveying instrument <NUM> shown in <FIG> differs from the surveying instrument illustrated with reference to <FIG> above in that the light source <NUM> and the detector <NUM> of the calibration system <NUM> are mounted on and fixed to the alidade <NUM> rather than the base <NUM>. Still, the beam path between the light source <NUM> and the detector <NUM> comprises a portion extending between a component fixed to the optical measuring instrument <NUM> and a component fixed to the base <NUM>.

The light emitted from the light source <NUM> traverses a pinhole <NUM> from which it emerges as a thin collimated beam. This beam traverses a beam splitter <NUM>, wherein it is reflected from a semitransparent surface <NUM> of the beam splitter <NUM>. The light beam then traverses a collimating lens <NUM> and a beam splitter <NUM> while traversing a semitransparent surface <NUM> of the beam splitter <NUM> and is reflected at two inner surfaces of a prism <NUM> to enter a beam splitter <NUM>. The light beam is reflected from a semitransparent surface <NUM> of the beam splitter <NUM> to be emitted towards a mirror <NUM> which is fixed to the base <NUM>. The light beam is reflected from the mirror <NUM> and traverses the beam splitter <NUM> wherein it is transmitted through the semitransparent surface <NUM>. The light beam then traverses the beam splitter <NUM> wherein it traverses the semi-transparent surface <NUM> to be incident on a reflecting surface <NUM> of a mirror <NUM> fixed to the measuring instrument <NUM>. Light reflected from the mirror <NUM> travels back to the beam splitter <NUM> wherein it is reflected from the semitransparent surface <NUM> towards the beam splitter <NUM>. The light traverses the collimating lens <NUM> and the beam splitter <NUM> and is incident on the detector <NUM>.

Again, a set of plural measurements is performed at different rotational positions of the alidade <NUM> about the first axis <NUM> and different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> when the optical measuring instrument <NUM> is in a configuration in which the mirror <NUM> is in the lower position shown in full lines in <FIG>. For example, a set of sixteen measurements can be performed at four different rotational positions of the measuring instrument <NUM> and for different rotational positions of the alidade <NUM> such that the corresponding detected light positions on the detector <NUM> are arranged along straight lines <NUM> and circles <NUM> as shown in <FIG>. A radius r1 of a smallest possible circle <NUM> can be determined from this set of measurements.

Thereafter, the optical measuring instrument <NUM> is rotated about the second axis <NUM> by about <NUM>° such that the mirror <NUM> is in the upper position shown in broken lines in <FIG>. The mirror <NUM> again provides the component of the beam path fixed to the measuring instrument <NUM>.

Again, a set of plural measurements is performed at different rotational positions of the alidade about the first axis and different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> when the optical measuring instrument <NUM> is in the configuration in which the mirror <NUM> is in the upper position shown in broken lines in <FIG>. For example, a set of sixteen measurements can be performed with four different rotational positions of the measuring instrument <NUM> and for different rotational positions of the alidade <NUM> such that the corresponding detected light positions on the detector <NUM> are arranged along straight lines <NUM> and circles <NUM> as shown in <FIG>. A radius r2 of a smallest possible circle <NUM> can be determined from this set of measurements.

The trunnion axis error k of the surveying instrument <NUM> can be determined using formulas (<NUM>) and (<NUM>) above based on the values of r1 and r2 obtained from the two sets of measurements.

The optical measuring instrument <NUM> is then orientated about the second axis <NUM> to assume an orientation as shown in <FIG> such that the light generated by a measuring light source (not shown in <FIG>) of the optical measuring instrument <NUM> is directed downwards along the first axis <NUM>.

This light beam is incident on the beam splitter <NUM>, and a portion of it is reflected from the semitransparent surface <NUM> of the beam splitter <NUM> such that it traverses the beam splitter <NUM> to be incident on the detector.

A set of plural measurements is performed at different rotational positions of the alidade <NUM> about the first axis <NUM> and different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> when the optical measuring instrument <NUM> is in the configuration in which measuring axis <NUM> is oriented substantially parallel to the first axis <NUM>. For example, a set of sixteen measurements can be performed with four different rotational positions of the measuring instrument <NUM> and for different rotational positions of the alidade <NUM> such that the corresponding detected light positions on the detector <NUM> are arranged along straight lines <NUM> and circles <NUM> as shown in <FIG>. A radius r3 of a smallest possible circle <NUM> can be determined from this set of measurements.

The collimation error c of the surveying instrument <NUM> can then be determined using formula (<NUM>) based of the determined radius r3 and the previously determined trunnion axis error k of the surveying instrument <NUM>.

<FIG> schematically illustrates a surveying instrument <NUM> according to a third embodiment comprising a calibration system <NUM> which can be used to determine some errors of the surveying instrument <NUM>. The surveying instrument <NUM> shown in <FIG> is similar to the surveying instruments illustrated with reference to <FIG> in that it comprises a base <NUM>, an alidade <NUM> rotatable relative to the base <NUM> about a first axis <NUM>, and an optical measuring instrument <NUM> rotatable relative to the alidade <NUM> about a second axis <NUM>. The surveying instrument <NUM> is also configured to provide a calibration beam path having a portion extending between a component fixed to optical measuring instrument <NUM> and a component fixed to the base <NUM>. This calibration beam path exists for two different ranges of rotational positions of the optical measuring instrument <NUM> about the second axis <NUM>.

The surveying instrument <NUM> shown in <FIG> differs from the surveying instrument illustrated with reference to <FIG> above in that a light source <NUM> of the optical measuring instrument <NUM> is used to generate the measuring light beam for all measurements and that a separate light source of the calibration system (light source <NUM> in <FIG>, <FIG>, <FIG> and <FIG>) is not provided.

The optical measuring instrument <NUM> of the surveying instrument <NUM> shown in <FIG> is oriented such that the measuring axis is oriented substantially parallel to the first axis <NUM>, and measuring light generated by the light source <NUM> of the optical measuring instrument <NUM> is directed towards the alidade <NUM> and base <NUM>. The light beam emitted from a front lens <NUM> of the optical measuring instrument <NUM> is incident on a prism <NUM> having an internal semitransparent surface <NUM> and a reflecting inner surface <NUM> arranged at a distance from the semitransparent surface <NUM>. The light beam incident of the prism <NUM> in <FIG> traverses the prism <NUM> wherein it traverses the semitransparent surface <NUM> and is incident on a detector <NUM> fixed to the base <NUM>.

A set of plural measurements is performed at different rotational positions of the alidade about the first axis and different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> when the optical measuring instrument <NUM> is in the configuration in which the measuring axis <NUM> is oriented substantially parallel to the first axis <NUM>. For example, a set of sixteen measurements can be performed with four different rotational positions of the measuring instrument <NUM> about the second axis <NUM> and four different rotational positions of the alidade <NUM> about the first axis <NUM> such that the corresponding detected light positions on the detector <NUM> are arranged along straight lines and circles, similar to what is shown in <FIG>, <FIG> and <FIG>, for example. A radius r1 of a smallest possible circle <NUM> can be determined from this set of measurements.

Thereafter, the optical measuring instrument <NUM> of the surveying instrument <NUM> shown in <FIG> is oriented as shown in <FIG> where the light beam emitted from the optical measuring instrument <NUM> is incident on the reflecting inner surface <NUM> of the prism <NUM>. The reflecting inner surface <NUM> is oriented such that the light beam reflected from the reflecting inner surface <NUM> is incident on the semitransparent surface <NUM> of the prism <NUM> and reflected therefrom towards the detector <NUM>.

Again, a set of plural measurements is performed at different rotational positions of the alidade <NUM> about the first axis <NUM> and different rotational positions of the optical measuring instrument <NUM> about the second axis <NUM> when the optical measuring instrument <NUM> is in the configuration in which measuring axis <NUM> is oriented transverse to the first axis <NUM> as shown in <FIG>. For example, a set of sixteen measurements can be performed with four different rotational positions of the measuring instrument <NUM> and four different rotational positions of the alidade <NUM> such that the corresponding detected light positions on the detector <NUM> are arranged along straight lines <NUM> and circles <NUM>, similar to what is shown in <FIG>, <FIG> and <FIG>, for example. A radius r2 of a smallest possible circle <NUM> can be determined from this set of measurements.

The radii r1 and r2 can be advantageously used to determine errors of the surveying system <NUM>. In formulas (<NUM>) and (<NUM>) above, r1 and r2 were used to determine the trunnion axis error k of the surveying instrument <NUM> and the collimation error cx of the mirror <NUM>. It was assumed that the collimation error cx of the mirror <NUM> entered formulas (<NUM>) and (<NUM>) with opposite signs since the two rotational positions of the measuring instrument relative to the alidade were opposite positions differing by <NUM>°. In the configurations shown in <FIG>, the measurement is not made against an additional mirror (mirror <NUM>) fixed to the measuring instrument <NUM> but by using the light source of the measuring instrument <NUM> itself. Therefore, it is the collimation error c of the surveying system <NUM> rather the collimation error cx of the mirror <NUM> which affects the measurements, and this error does contributes to the two sets of measurements with weights which are different from +<NUM> and -<NUM> as in formulas (<NUM>) and (<NUM>). Accordingly, the radii r1 and r2 for the configurations shown in <FIG> can be expressed as follows: <MAT> <MAT> wherein u represents a constant associated with the design of the surveying system <NUM>. This constant u covers the difference in the angles of rotation of the measuring instrument <NUM> about the second axis <NUM> in the configurations shown in <FIG> and can be determined in advance for the design of the surveying system <NUM>.

<FIG> shows the optical measuring instrument <NUM> shown in <FIG>, <FIG> and <FIG> in a fourth orientation about the second axis <NUM> relative to the alidade <NUM>. In this orientation, the measuring instrument <NUM> is arranged such that a retroreflector <NUM> mounted on the measuring instrument <NUM> is arranged in the beam path of the calibration system <NUM>. The retroreflector <NUM> is generally an optical element configured such that an incident beam of light is reflected back to its source. Examples of suitable retroreflectors are a retroreflector of the corner type, a retroreflector of the spherical type and a retroreflector of the cat's eye type. The retroreflector <NUM> can be mounted on the optical measuring instrument <NUM> at any suitable location such that there exists an orientation of the optical measuring instrument <NUM> about the second axis <NUM> relative to the alidade <NUM> such that a beam path exists between the retroreflector <NUM> provided on the optical measuring instrument <NUM> and the light source <NUM> of the calibration system <NUM>. In the illustrated embodiment, the light source <NUM> of the calibration system <NUM> is provided on the base <NUM>, together with the detector <NUM> of the calibration system <NUM>. In other embodiments, the light source of the calibration system can be mounted on the alidade, such as in the embodiment illustrated with reference to <FIG> above, wherein a portion of the beam path of the calibration system <NUM> extends between a component mounted on the base and a component mounted on the alidade, or a component mounted on the base and the retroreflector <NUM> mounted on the measuring instrument <NUM>, for example.

Light generated by the light source <NUM> and emitted from the pinhole <NUM> is collimated by the lens <NUM>, reflected from the reflecting surface <NUM> of the beam splitter <NUM> such that a beam of measuring light is directed towards the retroreflector <NUM>. This beam is inverted in its direction by the retroreflector <NUM> such that it travels back towards the beam splitter <NUM>, which directs the beam to the lens <NUM> which focuses the beam on the detector <NUM>. The detection signals of the detector <NUM> can be evaluated in order to determine light positions indicating the location of incidence of the focused beam on the detector <NUM>.

Due to the nature of the retroreflector <NUM>, which reflects the incident beam in itself, the location of incidence of the focused beam on the detector <NUM> will not change when the rotational position of the optical measuring instrument <NUM> about the second axis <NUM> is changed, as long as the beam is incident on the retroreflector <NUM>. Moreover, the location of incidence of the focused beam on the detector <NUM> will also not change when the rotational position of the alidade <NUM> about the first axis <NUM> is changed.

The location of incidence of the focused beam on the detector <NUM> is determined by the position of the detector relative to an optical axis of the collimation lens <NUM>. Specifically, the location of incidence of the focused beam on the detector <NUM> corresponds to the location where the optical axis of the collimation lens <NUM> intersects the detector <NUM>.

<FIG> shows the location of incidence of the focused beam on the detector <NUM> in the configuration shown in <FIG> in the two-dimensional coordinate system already used in <FIG>, <FIG> and <FIG> at reference numeral <NUM>.

Reference numeral <NUM> in <FIG> indicates the location of the centers <NUM> of the circles derived from the measurements illustrated with reference to <FIG> above. In these measurements, the surveying instrument <NUM> is in the configuration shown in <FIG> in which the optical measuring instrument <NUM> is oriented about the second axis <NUM> such that the beam of light generated by the light source <NUM> of the optical measuring instrument <NUM> is focused on the detector <NUM>. In this configuration of the surveying instrument <NUM>, the location of the centers of the circles are determined by an angle between the optical axis of the collimation lens <NUM> and the first axis <NUM> of rotation of the alidade <NUM> about the base <NUM>. In particular, if the components of the surveying instrument <NUM> were arranged such that the optical axis of the collimation lens <NUM>, after folding by the reflecting surface <NUM> of the beam splitter <NUM>, exactly coincides with the first axis <NUM>, the locations <NUM> and <NUM> would coincide on the detector <NUM>. In practice, however, the optical axis of the collimation lens <NUM> is arranged at an angle different from zero relative to the first axis <NUM>, resulting in a distance between locations <NUM> and <NUM> on the detector <NUM>.

Reference numeral <NUM> in <FIG> indicates the location of the centers <NUM> of the circles derived from the measurements illustrated with reference to <FIG> above. In these measurements, the surveying instrument <NUM> is in the configuration shown in <FIG> in which the optical measuring instrument <NUM> is oriented about the second axis <NUM> such that the beam of light generated by the light source <NUM> and collimated by the collimation lens <NUM> is focused on the detector <NUM> subsequent to its reflection from the mirror surface <NUM> of the mirror <NUM> mounted on the measuring instrument <NUM>. When the optical axis of the collimation lens <NUM> is arranged at an angle different from zero relative to the first axis <NUM>, the beam of measuring light will travel under such angle relative to the first axis <NUM> when the beam is incident on the mirror <NUM>. This angle is multiplied by a factor of two due to the reflection from the mirror surface <NUM>, such that the centers <NUM> of the circles <NUM> of the measurements shown in <FIG> are arranged at location <NUM> on a line <NUM> extending through locations <NUM> and <NUM> at twice the distance from location <NUM> than location <NUM>.

Reference numeral <NUM> in <FIG> indicates the location of the centers <NUM> of the circles derived from the measurements illustrated with reference to <FIG> above. In these measurements, the surveying instrument <NUM> is in the configuration shown in <FIG> in which the optical measuring instrument <NUM> is oriented about the second axis <NUM> such that the beam of light generated by the light source <NUM> and collimated by the collimation lens <NUM> is focused on the detector <NUM> subsequent to its reflection from the mirror surface <NUM>' of the mirror <NUM>. Again, the reflection of the beam from the mirror surface <NUM>' has the same effect on the beam as the reflection from the mirror surface <NUM>, such that also the location <NUM> is arranged on the line <NUM> at twice the distance from location <NUM> than location <NUM>, and that the location <NUM> coincides with location <NUM>.

The measurements illustrated above with respect to <FIG>, <FIG> and <FIG> are performed to determine the radii r1, r2 and r3 entering into formulas (<NUM>), (<NUM>) and (<NUM>), respectively. As illustrated above, the determining of each of the radii r1, r2, and r3 required the determination of the centers <NUM> of circles <NUM>. The determination of each circle requires at least <NUM> measurements performed at different orientations of the alidade <NUM> about the first axis <NUM> at a same orientation of the measuring instrument <NUM> about the second axis <NUM>. Therefore, at least twelve measurements would be required in order to determine the three radii r1, r2 and r3. This process can be time consuming.

However, this process can be simplified when the information shown in <FIG> is used. The location <NUM> can be determined with one single measurement using the reflection from the retroreflector <NUM>. If one of the centers corresponding to locations <NUM>, <NUM> and <NUM> is determined by performing three measurements obtained at different orientations of the alidade <NUM> about the first axis <NUM> and same orientations of the measuring instrument <NUM> about the second axis <NUM>, the line <NUM> is precisely determined. It is then possible to determine the other centers of the circles by exploiting the fact that the locations <NUM> and <NUM> coincide and are arranged at twice the distance from location <NUM> than location <NUM>. Therefore, the number of measurements required to determine the radii r1, r2 and r3 can be significantly reduced.

A further embodiment of a method of calibrating a surveying instrument will be illustrated with reference to <FIG> below. This method intends to determine at least one property of a coordinate transformation between a coordinate system of the detector <NUM> of the optical measuring instrument <NUM> and a coordinate system of the surveying instrument <NUM> based on plural measurements.

The plural measurements are performed in the configuration where the optical measuring instrument <NUM> is in the third orientation illustrated above with reference to <FIG>. The measurements are performed using the light source <NUM> of the calibration system <NUM> for producing a light beam, and the detector <NUM> of the optical measuring instrument <NUM> for detecting light of the light beam. The beam path of the light beam extends from the light source <NUM> fixed to the base <NUM>, is reflected by the beam splitter <NUM>, traverses the objective lens <NUM> of the optical measuring system <NUM>, is reflected from the beam splitter <NUM> of the optical measuring instrument <NUM> and is incident on the detector <NUM> of the optical measuring instrument <NUM>.

The objective lens <NUM> may include a telescope comprising plural lens elements and an actuator <NUM> for displacing at least one of the plural lens elements in a direction indicated by an arrow <NUM> in <FIG>. The actuator <NUM> can be controlled by the controller <NUM> in order to change a focal length of the objective lens <NUM>. For any given setting of the focal length, the actuator <NUM> of the calibration system <NUM> can be controlled to adjust the collimation of the beam generated from light source <NUM> such that this beam generates a well-defined beam spot on the detector <NUM>.

<FIG> further shows a mirror <NUM> provided on the base to establish a beam path from the light source <NUM> of the optical measuring instrument <NUM> via the mirror <NUM> to the detector <NUM> of the optical measuring instrument <NUM>. Moreover, a beam path can also be established between the light source <NUM> the optical measuring instrument <NUM> to the detector <NUM> of the calibration system <NUM>.

<FIG> is an illustration of a detection surface <NUM> of the detector <NUM> of the optical measuring instrument <NUM>. The detection surface <NUM> includes an array of pixels <NUM>.

In the measurements, the beam path exists between the light source <NUM> of the calibration system <NUM> and the detector <NUM> of the optical measuring instrument <NUM> achieved in a configuration as shown in <FIG>, for example.

A first set of measurements is performed at plural different orientations of the alidade <NUM> about the first axis <NUM> and at a same first orientation of the optical measuring instrument <NUM> about the second axis <NUM>. For example, the orientation of the optical measuring instrument <NUM> about the second axis <NUM> can be <NUM> gon. Reference numerals <NUM> in <FIG> indicate positions on the detection surface <NUM> determined as the positions of the light beam based on the light intensities detected by the pixels <NUM> of the detector <NUM> in plural measurements of the first set of measurements.

Thereafter, the orientation of the optical measuring instrument <NUM> about the second axis <NUM> is changed to a second orientation. The second orientation can be <NUM> gon, for example. A second set of measurements is performed where the second orientation of the optical measuring instrument <NUM> about the second axis <NUM> is maintained constant while the orientation of the alidade <NUM> about the first axis <NUM> is changed between the measurements. Reference numerals <NUM> in <FIG> indicate positions on the detection surface <NUM> determined as the positions of the light beam based on the light intensities detected by the pixels <NUM> of the detector <NUM> in the second set of measurements.

Additional sets of measurements can be performed at additional constant orientations of the measuring instrument about the axis <NUM> and different orientations of the alidade <NUM> about the second axis <NUM>.

Reference numeral <NUM> in <FIG> indicates a center of a circle <NUM> fitted through the plural positions <NUM>. Similarly, reference numeral <NUM> in <FIG> indicates a center of a circle <NUM> fitted through the plural positions <NUM>.

Reference numeral <NUM> in <FIG> indicates a line fitted through the plural centers <NUM> and <NUM> of the circles <NUM> and <NUM>, respectively. The line <NUM> represents those locations on the detection surface <NUM> of the detector <NUM> where the first axis <NUM> intersects the detection surface. Herein, the intersection of the first axis <NUM> with the detection surface <NUM> is to be understood such that the first axis <NUM> is folded by the beam splitter <NUM> as it were a light beam.

Different positions on the line <NUM> correspond to different orientations of the optical measuring instrument <NUM> about the second axis <NUM> at a constant orientation of the alidade about the first axis <NUM>. Reference numeral <NUM> in <FIG> illustrates a line orthogonal to line <NUM> and intersecting center <NUM>, and reference numeral <NUM> in <FIG> illustrates a line orthogonal to line <NUM> and intersecting center <NUM>. In the illustrated example, the line <NUM> is at the orientation of <NUM> gon of the optical measuring instrument <NUM> about the second axis <NUM>, while the line <NUM> is at the orientation of <NUM> gon of the optical measuring instrument <NUM> about the second axis <NUM>.

Reference numeral <NUM> in <FIG> represents a line at the orientation of <NUM> gon of the optical measuring instrument <NUM> about the second axis <NUM> which can be determined by interpolation based on the lines <NUM> and <NUM>. The lines <NUM> and <NUM> can be used as the abscissa and ordinate of a suitable coordinate system of the surveying instrument <NUM>. Specifically, when the optical measuring instrument <NUM> is pointing to a distant object carrying lines which are vertically oriented, these lines are imaged onto lines on the detection surface <NUM> which are parallel to line <NUM>. Similarly, when this object carries horizontal lines, these lines are imaged onto lines on the detection surface <NUM> which are parallel to line <NUM>.

A suitable coordinate of the detector <NUM> is oriented according to the two arrangement directions of the pixels <NUM> of the array of pixels of the detector <NUM>. It is apparent that a transformation from the coordinate system of the detector <NUM> to the coordinate system of the surveying instrument can be determined based on the information obtained from the plural sets of measurements illustrated above.

<FIG> further shows a vector k oriented parallel to line <NUM> and attached to the point of intersection of lines <NUM> and <NUM>. The length of the vector k is determined based on the trunnion axis error k determined as illustrated above. The trunnion axis error is determined in angular units. A scale to be used for transforming angular units to distances on the detector can be determined, for example based on the distance between lines <NUM> and <NUM> on the detector, since these lines correspond to known orientations of the optical measuring instrument <NUM>, such as <NUM> gon and <NUM> gon in the illustrated example.

<FIG> further shows a vector c oriented parallel to line <NUM> and attached to the head of vector k. The length of the vector c is determined based on the collimation error c determined as illustrated above. The length of the sum of the vectors k and c corresponds to the sum of the trunnion axis error and the collimation error.

<FIG> further shows a vector i oriented parallel to line <NUM> and attached to the head of vector c. The length of the vector i is determined based on the vertical index error i determined as illustrated above.

A point <NUM> at the head of vector i in <FIG> represents a location on the detection surface <NUM> of the detector <NUM> onto which a particular location of the object is imaged.

This particular location is the location of the distant object onto which the measuring light beam is directed. The pixels or the pixel positioned around this point <NUM> are also referred to as the center pixel or center pixels of the detector <NUM>.

The procedure illustrated above can be repeated for plural settings of the focal length the objective lens <NUM> of the measuring instrument <NUM> by adjusting the position of the lens <NUM> of the calibration system <NUM> using the actuator <NUM> correspondingly. Therefore, the center pixel of the detector <NUM> can be determined in dependence of the focal length of the objective lens <NUM> of the measuring instrument <NUM>. The center pixel may change when the focal length is changed due to possible limitations in the accuracy of the movements of the lens elements of the objective lens <NUM>.

The principles of the embodiments illustrated above can be applied to other types of surveying instruments, such as theodolites, tachymeters, total stations, scanners, laser range finders and dumpy levels, for example.

Additional information relating to scanners having a rotatable mirror for orienting the measuring axis in various directions can be found in the co-pending patent application of the present applicant titled " SURVEYING SYSTEM AND ROTATING MIRROR FOR A SURVEYING SYSTEM" and published as <CIT>.

Claim 1:
A method of calibrating a surveying instrument (<NUM>),
wherein the surveying instrument (<NUM>) comprises:
a base (<NUM>);
an alidade (<NUM>) rotatable about a first axis (<NUM>) relative to the base (<NUM>); and
an optical measuring instrument (<NUM>) having a measuring axis (<NUM>), wherein the optical measuring instrument (<NUM>) is rotatable about a second axis (<NUM>) relative to the alidade (<NUM>);
wherein the method comprises:
providing a beam path for a light beam using components including a light source (<NUM>) for emitting the light beam, zero or more lenses (<NUM>) for collimating the light beam, zero or more mirrors (<NUM>, <NUM>) for folding the beam path, zero or more beam splitters (<NUM>), and a position-sensitive detector (<NUM>) for detecting light of the light beam, wherein the light source is fixed to one of the base, the alidade and the optical measuring instrument, wherein the detector is fixed to one of the base, the alidade and the optical measuring instrument, wherein at least a portion of the beam path extends between one of the components, which is fixed to the base, and one of the components, which is fixed to the optical measuring instrument, and wherein the beam path exists for at least a first range of rotational positions of the optical measuring instrument about the second axis;
performing plural measurements; and
determining at least one error of the surveying instrument based on the plural measurements;
wherein each measurement includes detecting, using the detector, light of the light beam traveling from the light source along the beam path to the detector when the alidade is in a given rotational position about the first axis and the optical instrument is in a given rotational position about the second axis.