CN100588897C - Apparatus and method for measuring road bed sedimentation from long distance by laser - Google Patents

Apparatus and method for measuring road bed sedimentation from long distance by laser Download PDF

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CN100588897C
CN100588897C CN200810222753A CN200810222753A CN100588897C CN 100588897 C CN100588897 C CN 100588897C CN 200810222753 A CN200810222753 A CN 200810222753A CN 200810222753 A CN200810222753 A CN 200810222753A CN 100588897 C CN100588897 C CN 100588897C
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laser
measuring
sedimentation
stake
point
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CN101373132A (en
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冯其波
杨婧
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Beijing Jiaotong University
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Abstract

The invention relates to a device and a method for remotely measuring subgrade settlement by utilizing a laser and belongs to the technical field of optical measurement and geometric position measurement. The device of the invention comprises a settlement monitoring pile consisting of a bottom plate (501) and a measuring rod (502), a point light (1), a fixed observation pile (6), a laser measuringunit (2), a measuring signal transmission unit (3), a central processing unit (7) and power supply modules (401 and 402). The method comprises the following steps: the settlement monitoring pile is buried in a point to be measured and the point light is arranged on the settlement monitoring pile, so that the point light and the subgrade of the point to be measured settle synchronously; the pointlight is imaged through a lens (201) of the laser measuring unit, and an image point A'is positioned on a photoelectric detector (202); and the displacement of the object point of the light can be calculated through the displacement of the image point, that is, the subgrade settlement amount of the point to be measured. The invention has high measurement precision, can implement the settlement measurement in the construction process or after the construction, and the remote settlement measurement of any positions and any depth of a subgrade.

Description

A kind of apparatus and method of utilizing the laser remotely measuring subgrade settlement
Technical field
The invention belongs to optical measurement and geometric position field of measuring technique, relate to a kind of apparatus and method of utilizing the laser remotely measuring subgrade settlement.
Background technology
Subgrade settlement all is difficult to avoid in the work progress of road and after the completion.Because sedimentation, non-uniform settling, the track that can cause sink and the rail level bending, influence the ride comfort of circuit; By in the track of bridge, can cause the differential settlement of abutment and roadbed, when train crosses these locations, because orbit rigidity and distortion that sedimentation causes are undergone mutation, make the dynamic action between wheel track increase, thereby cause that track destroys, the stationarity and the security of influence driving.In order in time to understand sedimentation and the sedimentation variation tendency of roadbed under load action, so that adopt an effective measure in advance, prevent the generation of accident, need and complete in the work progress of road is provided with settlement observation later on one period.Completion back settlement observation will be determined observation time length according to actual conditions.
Along with the fast development of orbit construction, relevant safety problem more and more obtains people's attention in recent years.The particularly appearance of high-speed railway has now had higher requirement to the control of roadbed deformation, thereby has also made measurement, calculating and the control of subgrade settlement seem even more important.And in this three, the measurement of sedimentation is both foundation and basis of back.Yet, to measure with respect to artificial subgrade settlement, equipment that can remotely measuring subgrade settlement will be the development trend that subgrade settlement is measured.
Be used for measurement road subgrade settlement observation device at present and mainly contain water tumbler sedimentometer, settlement plate measurement mechanism, section sedimentometer, pvc pipe sedimentometer, magnet ring sedimentometer.
Water tumbler sedimentometer law of connected vessels is mapped to the roadbed outside to inner certain any the elevation of roadbed, so measure the elevation that the elevation of this mapping point of roadbed outside is promptly known roadbed internal observation point.Its measuring system comprises that Settlement Cup, observation cup, pipeline comprise flexible duct, valve and connector, and Settlement Cup and observation cup are by pipeline connection, and liquid is equipped with in the inside.For example the patent No. is 200520044774.0, name is called the Chinese patent of " a kind of sedimentometer ", settlement cell is placed roadbed or works bottom, and the graduated tube chi is placed outside roadbed or the works, outside roadbed or works, obtain the sedimentation of roadbed or works.This system with the roadbed outside a bit, promptly observation cup position is as reference point, and its weak point is, is connected by pipeline between measurement point and the reference point, if, will influence the accuracy of measurement result because extraneous factor causes flexible duct expansion or pipeline seepage etc.In addition, observation cup position is far away more from roadbed, and this position is because the suffered influence of construction is more little, but can increase the cost of burying pipeline underground simultaneously.
The settlement plate base of settlement plate measurement mechanism by the measuring staff that links to each other with base, can record the subgrade settlement value that base is buried the place underground along with subgrade settlement.Before measuring, must bury corresponding leveling point underground to each settlement plate, through one period stabilization time system-wide section leveling point being carried out translocation, make each leveling point on a benchmark elevation, referring to Wang Zumin, Wu Xianzhang, " Su Jia Hangzhoupro Freeway Soft settlement of foundation observation operational method ", " East China highway " the 2nd phase in 2006.Owing to be manual measurement, increased workload and cost, and precision is affected easily.
The pvc pipe sedimentometer claims that also tiltmeter is a kind of mensuration dip angle of hole and azimuthal in-situ monitoring instrument.Measure the inclination angle at place, probe place by Sensitive Apparatus, convert the inclination angle to level or perpendicular displacement by certain relational expression, add up then and obtain the distance of measured point and initial position line, again to the different times The contrast analysis of measured, the result that can determine the level of each soil layer or perpendicular displacement is (referring to Zhang Hongchun, Hou Jianjun, " application of pvc pipe section sedimentometer in express highway roadbed settlement observation ", " highway " 2007 the 8th phases, Chang Jianmei, Zhao Yucheng, Feng Huaiping, " application of horizontal inclinometer in subgrade settlement is measured ", " Shanxi architecture " 2004 the 16th phases).The benchmark of this measuring method is exactly the initial position line of pvc pipe, its accuracy of measurement is relevant with burying underground of pipe, and what record also is a relative settlement amount, if record data to several pvc pipes compares, also must set up a unified benchmark with other method.
The magnet ring sedimentometer is a kind of delaminating deposition instrument, used sensor is to design according to electromagnetic induction principle, magnetic induction sedimentation ring is imbedded underground each point position to be measured by bore mode in advance, when sensor during by the magnetic induction ring, produce electromagnetic induction signal and deliver to the ground instrument demonstration, send sound and light alarm simultaneously.Read the scale numerical value of corresponding steel ruler on the gauge point of aperture, be the degree of depth of sedimentation ring.General each measured value subtracts each other the relative settlement amount that is this measuring point with measured value last time.For obtaining the absolute settlement amount, generally with bottom sedimentation cursor position as the monitoring criteria point, by to the different times The contrast analysis of measured, can determine the sedimentation of each soil layer or swell the result (referring to Zhao Hongyong, Liu Jiankun, Cui Jiangyu, " understanding and the evaluation of high-speed railway subgrade settlement monitoring method ", the 6th phase of " subgrade engineering " calendar year 2001).This method is the position to be marked in the sedimentation of the bottom be considered as fixed point, make its real not sedimentation, generally the hole will be beaten very dark, has increased operation easier and cost like this.
Summary is got up, and following three major defects of prior art ubiquity: (1) relies on manual measurement or record, and efficiency of measurement is low, and accuracy of detection is low; (2) during selection reference point, stability and low cost can not get both; (3) measuring can not remote monitoring, can not measure automatically.
Summary of the invention
Primary and foremost purpose of the present invention is to provide a kind of device that utilizes the laser remotely measuring subgrade settlement.This device utilizes advanced laser measuring technique to realize, can carry out remote auto to the sedimentation of roadbed and measure, and can reach submillimeter level even higher measuring accuracy.
A further object of the invention provides the method for utilizing the measurement device subgrade settlement of laser remotely measuring subgrade settlement by above-mentioned.This method can realize the remote measurement of sedimentation in the subgrade construction process, also can realize the remote measurement of settlement after construction, can also realize the robotization of measuring by certain processing; Also can under the situation of influence construction hardly, carry out remote measurement to the sedimentation of roadbed optional position and appropriate depth.
For realizing above-mentioned goal of the invention, the present invention adopts following technical scheme:
A kind of device that utilizes the laser remotely measuring subgrade settlement, this device comprises subgrade settlement measuring unit, measuring-signal transmission unit, CPU (central processing unit) and power module, connects in wired or wireless mode between measuring-signal transmission unit and the CPU (central processing unit).
Described subgrade settlement measuring unit comprises: pointolite, laser measurement unit, sedimentation detect stake and fixing observation stake.
Described pointolite is installed in described sedimentation and detects in the stake, and sedimentation detects stake and is embedded in the tested point place; Described laser measurement unit is installed in sedimentation and detects in the corresponding fixing observation stake of stake, and fixing observation stake is installed in beyond the subgrade settlement distorted area, sedimentation or its settling amount does not take place compare the place of ignoring with the measured point; Or described pointolite is installed in fixing the observation in the stake, and the laser measurement unit is installed sedimentation and detected in the stake; Adjust the relative position between pointolite and the laser measurement unit, pointolite is arranged on the optical axis of laser measurement unit imaging len, and after making the imaging len imaging of light in the laser measurement unit that pointolite sends, picture point A ' is positioned at the center of photoelectric position detector.
Described laser measurement unit is made up of imaging len, photoelectric position detector, signal processor, mounting box.Described imaging len and photoelectric position detector are fixed in the described mounting box by two supports respectively, and make the optical axis of imaging len vertical substantially with the photosurface of photoelectric position detector.
Described laser measurement unit is made up of imaging len, photoelectric position detector, signal processor, mounting box; Described imaging len and photoelectric position detector are fixed in the described mounting box by two supports respectively, and make the optical axis of imaging len vertical with the photosurface of photoelectric position detector.
Described pointolite is made up of red light emitting diodes, the aperture of high brightness, perhaps directly uses semiconductor laser to form or use the semiconductor laser of magnetic tape trailer fibre.
Described photoelectric position detector adopts any one in linear charge-coupled array or surface array charge-coupled device or four-quadrant photo detector or the Position-Sensitive Detector.
Described sedimentation detects stake to be made up of base plate and measuring staff, and measuring staff bottom vertical fixing is on base plate, and the measuring staff top is above the ground level; Or sedimentation detection stake is directly built at road bed by cement or other materials.
Based on a kind of method of utilizing the laser remotely measuring subgrade settlement that the above-mentioned device that utilizes the laser remotely measuring subgrade settlement is realized, its step:
Step 1, use laser range finder or directly with tape measure go out described pointolite to the imaging len center of described laser measuring device for measuring apart from s.
Step 2, when roadbed generation sedimentation, sedimentation detects stake sedimentation thereupon, be placed in the displacement h of the pointolite generation same distance on its measuring staff, the pointolite that pointolite produces sees through imaging len imaging on photoelectric position detector corresponding displacement h ' also takes place thereupon, and this displacement obtains by signal processor.
Step 3, the object distance s and known imaging len focal distance f, the scioptics imaging formula again that record according to step 1
Figure C20081022275300081
Calculate image distance
Figure C20081022275300082
Step 4, according to object distance s, the image point displacement amount h ' that step 2 records that step 1 records, step 3 is calculated the image distance s ' of gained, by the relation between three and the pointolite displacement
Figure C20081022275300083
Calculate the pointolite displacement
Figure C20081022275300084
Thereby obtain the subgrade settlement amount h in this moment of tested point.
The present invention compared with prior art, the beneficial effect that is had is:
One adopts laser measurement subgrade settlement, has not only avoided human error, and measuring accuracy also increases.
Its two, in subgrade settlement is measured, preferentially adopt modern wireless telecommunications means that measured information is delivered to CPU (central processing unit), reduced the surveying work amount, improved efficiency of measurement.
Its three, adopt remote, non-contacting measurement, when selecting the subgrade settlement reference point, can guarantee the stability and the lower cost of reference point simultaneously.
Its four, adopt the lens imaging principle, photoelectric position detector is measured than the bigger subgrade settlement value of self range ability.
The present invention detects the sensitivity of subgrade settlement less than 0.1mm, detects error less than 0.5mm, can realize the automatic monitoring to subgrade settlement simultaneously for a long time.
Description of drawings
The present invention is further illustrated below in conjunction with the drawings and specific embodiments.
Fig. 1 is a kind of measurement index path that utilizes the device of laser remotely measuring subgrade settlement.
Fig. 2 is a kind of composition synoptic diagram that utilizes the device of laser remotely measuring subgrade settlement of embodiment one.
Fig. 3 is the synoptic diagram of three kinds of pointolites.
Fig. 4 is the composition synoptic diagram of CPU (central processing unit).
Fig. 5 is a kind of composition synoptic diagram that utilizes the device of laser remotely measuring subgrade settlement of embodiment two.
Among the figure:
Pointolite 1, laser measuring device for measuring 2, data transmission unit 3, sedimentation detects stake 5, fixing stake 6, CPU (central processing unit) 7, tested place roadbed 8, the red high brightness LED 101 observed, aperture 102, semiconductor laser 103,104, tail optical fiber 105, stationary installation 106, imaging len 201, photoelectric position detector 202, mounting box 203, signal processor 204, support 205,206, power module 401,402, sedimentation detect stake measuring staff base plate 501, and sedimentation detects stake measuring staff 502.
Embodiment
Embodiment one
Introduce the inner sedimentation device of the remote measurement roadbed that utilizes laser measuring technique to realize below.
As shown in Figure 2, the inner sedimentation device of this laser remote measurement roadbed mainly is made up of subgrade settlement measuring unit, measuring-signal transmission unit, CPU (central processing unit) and power module, is connected with wired or wireless mode between measuring-signal transmission unit and the CPU (central processing unit).Wherein, the subgrade settlement measuring unit is the basis of realizing the inner sedimentation of laser remote measurement roadbed, and it comprises that pointolite 1, laser measurement unit 2, sedimentation detect stake 5 and fixing 6 four parts of stake of observing.
Pointolite 1 is made up of High brightness Red LED 101, aperture 102, shown in Fig. 3 (a), is fixed on sedimentation and detects on the measuring staff 502 of stake 5, and wherein High brightness Red LED 101 links to each other with power module 401; Perhaps directly use semiconductor laser 103, shown in Fig. 3 (b), be fixed on sedimentation and detect on the measuring staff 502 of stake 5, semiconductor laser 106 links to each other with power module 401; Perhaps directly use the semiconductor laser of magnetic tape trailer fibre, form by semiconductor laser 104, tail optical fiber 105, stationary installation 106, shown in Fig. 3 (c), being fixed on sedimentation detects on the measuring staff 502 of stake 5, special optical fiber pigtail 105 front ends are fixing by stationary installation 106, and wherein semiconductor kistributed-feedback laser 104 links to each other with power module 401.
Laser measurement unit 2 is made up of imaging len 201, photoelectric position detector 202, signal processor 204, mounting box 203, it is arranged on the position that can detect the pointolite that pointolite 1 sends, is directly installed on sedimentation to detect in corresponding fixing observations of stake 56.Imaging len 201 is fixed in the mounting box 203 by support 206, photoelectric position detector 202 is fixed in the mounting box 203 by support 205, photoelectric position detector 202 adopts any one in linear charge-coupled array or surface array charge-coupled device or four-quadrant photo detector or the Position-Sensitive Detector, signal processor 204 directly is fixed in the mounting box 203, mounting box 203 sealings.Photoelectric position detector 202, signal processor 204, measuring-signal transmission unit 3 are linked in sequence.Pointolite 1 is arranged on the optical axis of laser measurement unit imaging len, and the light that sends is by the transparent window in the mounting box 203, via after imaging len 201 imagings, and picture point A ' is positioned at the center of photoelectric position detector 202.Signal processor 204 is made up of pre-amplification circuit, position signalling treatment circuit, three functional modules of data transformation interface circuit, and these three functional modules are linked in sequence.Photoelectric position detector 202 links to each other with signal processor 204, measures the picture point A ' position change amount h ' vertically of pointolite 1 automatically by signal processor 204, and initial position h ' is 0.
Sedimentation detects stake 5 to be made up of base plate 501 and measuring staff 502, as shown in Figure 2.Measuring staff 502 bottom vertical fixing are on base plate 501, and the top is above the ground level.The space of a whole page area of base plate is usually slightly larger than the twice of measuring staff cross-sectional area, decide according to the situation of burying place's roadbed underground, the density of roadbed is more little, and base plate space of a whole page area is big more, otherwise more little, guarantee sedimentation detection stake 5 and bury place's subgrade settlement underground to produce the synchronization position variation.
Fixing observe stake 6 and build in that sedimentation or its settling amount do not take place and compare negligible place with the measured point, as the reference point of measuring.
The measuring-signal transmission unit is a data transmission unit 3, is connected with laser measurement unit 2.This signal transmission unit transmits measured data with wired or wireless mode to CPU (central processing unit) 7.
CPU (central processing unit) 7 mainly is made up of measurement data receiver module, calculation processing unit, software processing system, demonstration and four functional modules of storage as shown in Figure 4.These four functional modules are linked in sequence.The data that CPU (central processing unit) 7 received signal transmission units transmit are handled to obtain the subgrade settlement value it.
Interchange or DC voltage that power module 401,402 is used for the circuit limit is provided obtain voltage of voltage regulation by processing such as conversion, power module 401 is installed on sedimentation and detects in the stake 5, the working power of above-mentioned pointolite 1 is provided, power module 402 is installed on fixing the observation in the stake 6, and above-mentioned laser measurement unit 2, the working power of data transmission unit 3 are provided.
Next introduce the device that utilizes the inner sedimentation of above-mentioned laser remote measurement roadbed, realize the method for the inner sedimentation of laser remote measurement roadbed, its step is as follows:
Step 1, the pointolite that uses laser range finder or directly go out pointolite 1 with tape measure to imaging len 201 centers of laser measurement unit 2 apart from s.
Step 2, when roadbed generation sedimentation, sedimentation detects stake 5 sedimentations thereupon, be placed in the displacement h of the pointolite 1 generation same distance on its measuring staff 502, the pointolite that pointolite 1 produces sees through imaging len 201 imaging on photoelectric position detector 202 corresponding displacement h ' also takes place thereupon, and this displacement obtains by signal processor 204.
Step 3, the object distance s and known imaging len focal distance f, the scioptics imaging formula again that record according to step 1
Figure C20081022275300111
Get image distance
Figure C20081022275300112
Step 4, according to object distance s, the image point displacement amount h ' that step 2 records that step 1 records, step 3 is calculated the image distance s ' of gained, can be by the relation between three and the pointolite displacement
Figure C20081022275300121
Calculate the pointolite displacement
Figure C20081022275300122
Thereby obtain the subgrade settlement amount h in this moment of tested point.
Wherein step 3, step 4 are carried out in CPU (central processing unit) 7.
Above-mentioned a kind of apparatus and method of utilizing the laser remotely measuring subgrade settlement, be for a long time the continuous coverage data of roadbed settlement measuring device to be sampled by CPU (central processing unit) 7, obtain the inner settlement measurement value of roadbed, realize long-term uninterrupted monitoring the sedimentation of roadbed inside.
Embodiment two
Introduce the remote measurement road bed sedimentation device that utilizes laser measuring technique to realize below.
As shown in Figure 5, this laser remote measurement road bed sedimentation device is similar to the inner sedimentation device of laser remote measurement roadbed, mainly form, connect with wired or wireless mode between measuring-signal transmission unit and the CPU (central processing unit) by subgrade settlement measuring unit, measuring-signal transmission unit, CPU (central processing unit) and power module.Wherein, the subgrade settlement measuring unit is the basis of realizing the sedimentation of laser remote measurement road bed.It comprises that pointolite 1, laser measurement unit 2, sedimentation detect stake 5 and fixing 6 four parts of stake of observing.
The inner sedimentation device of measuring-signal transmission unit in the laser remote measurement road bed sedimentation device, power module and laser remote measurement roadbed is identical, seldom gives unnecessary details at this, launches explanation with regard to the subgrade settlement measuring unit below.
Pointolite 1 is made up of High brightness Red LED 101, aperture 102, shown in Fig. 3 (a), is fixed on sedimentation and detects in the stake 5, and wherein High brightness Red LED 101 links to each other with power module 401; Perhaps directly use semiconductor laser 103, shown in Fig. 3 (b), be fixed on sedimentation and detect in the stake 5, semiconductor laser 106 links to each other with power module 401; Perhaps directly use the semiconductor laser of magnetic tape trailer fibre, form by semiconductor laser 104, tail optical fiber 105, stationary installation 106, shown in Fig. 3 (c), being fixed on sedimentation detects in the stake 5, special optical fiber pigtail 105 front ends are fixing by stationary installation 106, and wherein semiconductor kistributed-feedback laser 104 links to each other with power module 401.
Laser measurement unit 2, fixing observation stake 6 and the inner sedimentation device of laser remote measurement roadbed are identical, seldom give unnecessary details at this.
Sedimentation detects stake 5 and directly builds at tested point place road bed, with the subgrade settlement generation synchronization position variation of build place.
Utilize above-mentioned laser remote measurement road bed sedimentation device to realize the method for laser remote measurement road bed sedimentation, realize that with utilizing the inner sedimentation device of laser remote measurement roadbed the method step of the inner sedimentation of laser remote measurement roadbed is identical, seldom give unnecessary details at this.
Above-mentioned a kind of apparatus and method of utilizing the laser remotely measuring subgrade settlement, be for a long time the continuous coverage data of roadbed settlement measuring device to be sampled by CPU (central processing unit) 7, obtain road bed settlement measurement value, realize long-term uninterrupted monitoring the road bed sedimentation.
The device of above-mentioned laser remotely measuring subgrade settlement is fit to open-air circuit is carried out remote detection.When carrying out remote detection, the subgrade settlement measurement mechanism carries out continuous coverage, for a long time the data of measuring gained is sampled by CPU (central processing unit) 7, obtains the subgrade settlement amount, if CPU (central processing unit) 7 is programmed, can also realize the robotization that detects.
When carrying out remote detection, the measuring-signal transmission unit in the device of each laser remotely measuring subgrade settlement preferably uses communication to be connected with CPU (central processing unit).Use communication can significantly reduce the realization cost of this subgrade settlement laser measurement system.

Claims (5)

1. device that utilizes the laser remotely measuring subgrade settlement, this device comprises, subgrade settlement measuring unit, measuring-signal transmission unit, CPU (central processing unit) and power module connect in wired or wireless mode between measuring-signal transmission unit and the CPU (central processing unit); It is characterized in that:
Described subgrade settlement measuring unit comprises: pointolite (1), laser measurement unit (2), sedimentation detect a stake (5) and fixing observe (6);
Described pointolite (1) is installed in described sedimentation and detects in the stake (5), and sedimentation detects stake (5) and is embedded in the tested point place; Described laser measurement unit (2) is installed in sedimentation and detects in corresponding fixing observations stake (6) of stake (5), and fixing observation (6) is installed in beyond the subgrade settlement distorted area, sedimentation does not take place or compare the uncared-for place of settling amount with the measured point; Or described pointolite (1) is installed in fixing the observation in the stake (6), and laser measurement unit (2) are installed in sedimentation and detect in the stake (5); Adjust the relative position between pointolite (1) and laser measurement unit (2), pointolite (1) is arranged on the optical axis of laser measurement unit (2) imaging len (201);
Described laser measurement unit (2) is made up of imaging len (201), photoelectric position detector (202), signal processor (204), mounting box (203);
Described imaging len (201) and photoelectric position detector (202) are fixed in the described mounting box (203) by two supports respectively, and make the optical axis of imaging len (201) vertical with the photosurface of photoelectric position detector (202).
2. a kind of device that utilizes the laser remotely measuring subgrade settlement according to claim 1, it is characterized in that: described pointolite (1) is made up of red light emitting diodes, the aperture of high brightness, perhaps directly uses the semiconductor laser of semiconductor laser or use magnetic tape trailer fibre.
3. a kind of device that utilizes the laser remotely measuring subgrade settlement according to claim 1 is characterized in that: described photoelectric position detector (202) adopts any one in linear charge-coupled array or surface array charge-coupled device or four-quadrant photo detector or the Position-Sensitive Detector.
4. a kind of device that utilizes the laser remotely measuring subgrade settlement according to claim 1, it is characterized in that: described sedimentation detects stake (5) and is made up of base plate (501) and measuring staff (502), measuring staff (502) bottom vertical fixing is on base plate (501), and measuring staff (502) top is above the ground level; Or sedimentation detection stake is directly built at road bed by cement or other materials.
5. method of utilizing the described laser remotely measuring subgrade settlement of claim 1 device to realize the laser remotely measuring subgrade settlement is characterized in that may further comprise the steps:
Step 1, measurement point light source (1) to imaging len (201) center apart from s;
Step 2, measurement point light source (1) is at the displacement h ' of the last picture point of photoelectric position detector (202), and this displacement obtains by signal processor (204);
Step 3 is calculated image distance s ', s ′ = sf s - f , F is the focal length of imaging len (201);
Step 4 is calculated subgrade settlement amount h, h = s s ′ · h ′ , The image point displacement that h ' records for laser measurement unit (2).
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