Measured Tilt Angles Research Articles

Novel Pedicle Navigator Based on Micro Inertial Navigation System (MINS) and Bioelectric Impedance Analysis (BIA) to Facilitate Pedicle Screw Placement in Spine Surgery: Study in a Porcine Model.

Study Design.A porcine model.Objective.The study aims to design a novel pedicle navigator based on micro-inertial navigation system (MINS) and bioelectrical impedance analysis (BIA) to assist place pedicle screw placement and validate the utility of the system in enhancing pedicle screw placement.Summary of Background Data.The incidence of pedicle screw malpositioning in complicated spinal surgery is still high.Procedures such as computed tomography image-guided navigation, and robot-assisted surgery have been used to improve the precision of pedicle screw placement, but it remains an unmet clinical need.Methods.The miniaturized integrated framework containing MINS was mounted inside the hollow handle of the pedicle finder. The inner core was complemented by a high-intensity electrode for measuring bioelectric impedance. Twelve healthy male Wuzhishan minipigs of similar age and weight were used in this experiment and randomized to the MINS-BIA or freehand (FH) group. Pedicle screw placement was determined according to the modified Gertzbein–Robbins grading system on computed tomography images. An impedance detected by probe equal to the baseline value for soft tissue was defined as cortical bone perforation.Results.A total of 216 screws were placed in 12 minipigs. There were 15 pedicle breaches in the navigator group and 31 in the FH group; the detection rates of these breaches were 14 of 15 (93.3%) and 25 of 31 (80.6%), respectively, with a statistically significant difference between groups. The mean offsets between the planned and postoperatively measured tilt angles of the screw trajectory were 4.5° ± 5.5° in the axial plane and 4.8° ± 3.3° in the sagittal plane with the navigator system and 7.0° ± 5.1° and 7.7° ± 4.7°, respectively, with the FH technique; the differences were statistically significant.Conclusion.A novel and portable navigator based on MINS and BIA could be beneficial for improving or maintaining accuracy while reducing overall radiation exposure.

Absolute radiation pressure detector using a diamagnetically levitating test mass

We have developed an absolute radiometer to measure laser power by means of radiation pressure in a closed control-loop configuration using diamagnetically levitated pyrolytic graphite as the soft spring and gravity as a contactless restoring force. Our approach takes advantage of an extremely low spring stiffness (2.95 mN/m) afforded by diamagnetic levitation above a permanent magnet array and a lock-in amplifier in the feedback loop to attain a 30 m W r m s noise. A horizontally directed laser beam impinges on a highly reflective dielectric stack mirror mounted on the levitating pyrolytic graphite shuttle. The light’s momentum displaces the shuttle, and its position is restored by tilting the magnet array with a piezoelectric actuator. The closed-loop configuration avoids the need for accurate knowledge of the system spring stiffness or environmental dependencies of the diamagnetic levitation. Absolute laser power measured is traceable to the mass of the diamagnetically levitating shuttle system, the local gravitational acceleration, and the interferometrically measured tilt angle of the magnet array. The system is demonstrated with a laser power of 2.7 W, yielding a combined relative expanded uncertainty ( k = 2 ) of 1.9%. The upper limit of measurable power is determined by the range of the piezoelectric actuator, and the minimum power is currently limited by the noise floor that is constrained by air currents.

Electrochemical Tilt Sensors With Symmetric Concentric Electrode Pairs

This paper presented the principle, design, fabrication, and characterization of Molecular Electronic Transducer (MET) single-axis tilt sensors. The proposed sensor has a circular channel deposited with symmetric concentric electrode pairs and half-filled with a liquid electrolyte. Such inclination-dependent liquid level is detected by the differential current from the electrochemical reaction at the two symmetric concentric electrode pairs. In order to reduce the form factor, an organic solvent is added to the aqueous electrolyte to lower the surface tension force. Limited by the liquid motion and reaction rate, the sensors are capable to measure tilt angle under static conditions only. From the tilt angle stepping experiments, the performance of the proposed tilt sensors is characterized and compared. The sensors’ response time is dominated by the electrochemical equilibrium arrival time. They can achieve a low discrimination threshold of 0.016° and a short time constant of 0584s within the ±85° measurement range with a power consumption of less than 0.1mW. Compared to previously reported MET tilt sensors with a parallel swirl electrode configuration, the signal-to-noise ratio and response time are improved significantly.

NOA61-Polymer Fiber Fizeau Interferometer with a Flexible NOA65-Polymer Taper for Simultaneous Measurement of Tilt Angle and Temperature.

This study proposes and experimentally demonstrates a NOA61-polymer fiber Fizeau interferometer (PFFI) connected to a flexible NOA65-polymer taper (PT) for simultaneous measurement of tilt angle and temperature (T). The PT/PFFI fiber sensor consists of a taper-shaped flexible NOA65 polymer and single-mode fiber with an endface that is attached to a NOA61-polymer. The NOA61-polymer of PFFI is highly sensitive to variations of T with high repeatability and enables the simultaneous measurement of tilt angle by connecting with the highly flexible NOA65-PT. the interference fringe visibility of optical spectra in the PFFI can be highly controlled by the tilt angle of the PT and is thus capable of measuring tilt angles with high sensitivity. On the other hand, wavelength shifts of the spectra in the PFFI only occur when T varies. The proposed PT/PFFI can simultaneously detect the tilt state and the variation of surrounding T by measuring the optical spectral responses and eliminating cross sensitivity. Experimental results demonstrate the PT/PFFI can simultaneously measure tilt angles and T with good sensitivities and obtain averages of 0.4 dB/° and 0.17 nm/°C, respectively.

Receiver tilt: a scourge for aquatic telemetry or useful predictor variable

BackgroundWater current data can be a useful predictor variable to include in acoustic telemetry studies given its link to changes in fish behaviour. While there are a range of sensors which can measure currents, they are often expensive and logistically difficult to deploy and maintain. Contemporary acoustic receivers measure tilt angle which may act as a proxy for water current data if the receiver is moored on a rope and buoy system and allowed to sway in the direction of water flow. We tested the relationship between tilt angle and water current by co-locating two types of commonly deployed receivers with current meters.ResultsBoth receivers (Vemco VR4 and VR2AR) displayed similar ranges in tilt angle. While the VR4 could only measure tilt on a daily basis, the VR2AR measurements were taken hourly; these data were then also aggregated on a daily scale. A positive relationship was found between the tilt angle for both types of receivers and current speed, including for both aggregated daily and hourly data for the VR2AR. Both receivers tended to slightly over-estimate current at lower speeds and underestimate it at high speeds.ConclusionsThese data show tilt angles recorded by commonly deployed receivers could be incorporated as a proxy for current flow where dedicated current loggers are absent. We would recommend programming receivers to record tilt as frequently as possible to account for short-term variability in environmental conditions.

Tapered Polymer Fiber Inclinometers

This work proposes a novel, highly sensitive, and simple structure based on a tapered polymer as a tilt fiber sensor to sensitively measure tilt angles (θ).The fiber-optic tilt sensor consists of a tapered polymer and single-mode fibers (SMF), into which the tapered polymer to generate a bent in the sensor that is strongly correlated with θ. The used tapered polymer in the tilt sensing is the temperature (T) insensitive. It is further combined with a general fiber Bragg grating (FBG) as a temperature indicator for achieving simultaneous measurement of inclination (θ) and ambient T. The endface of the fiber is coated with a gold film to increase the light reflectivity and improve the measurement range. Experimental results show that when the sensor tilts, the reflective optical power changes significantly with high sensitivity, and the peak wavelength of FBG shifts when T varies. Both parameters can be measured simultaneously with good discrimination. An average tilt angle sensitivity of approximately 4.23 dB/deg. and a high resolution of 0.009 deg. are achieved in a θ variation from −6 to +6 deg. Simulations were performed and the numerical results were in good agreement with the experimental measurement.

Relationship Between Basal Plane Dislocation Distribution and Local Basal Plane Bending in PVT-Grown 4H-SiC Crystals

The inhomogeneous distributions of basal plane dislocations (BPDs) in PVT-grown 4H-SiC crystal boule due to internal stresses cause lattice plane bending, which strongly affect SiC-based device fabrication. The relationship between BPDs and local basal plane bending in 6-inch 4H-SiC substrates has been investigated. Synchrotron monochromatic beam x-ray topography (SMBXT) imaging shows black and white contrast of BPDs with Burgers vectors of opposite signs based on the principle of ray tracing. We have evaluated the net difference of BPDs with black and white contrast along both [11$$ \bar{2}$$0] and [1$$ \bar{1}$$00] radial directions on the Si face across multiple 6-inch diameter 4H-SiC substrates sliced from the same and different boules and predicted the nature (concave/convex) and amount of bending of the basal plane in these wafers. Line scans of 0008 reflection using high resolution x-ray diffractometry (HRXRD) has been carried out along the two directions to verify the nature of bending in these wafers. Results show quite different bending behavior along [11$$ \bar{2} $$0] and [1$$ \bar{1}$$00] directions, indicating that the Si face of 6-inch substrates creates non-isotropic bending on the basal plane. These observations are correlated quite well with net BPD density analysis. The physical shapes of the wafers were also measured to be not flat due to the surface effect. Quantitative analysis of the degree of basal plane bending based on the SMBXT data was carried out and found to be correlating well with the measured tilt angle from HRXRD. Existence of a high stress center was observed in one of the 6-inch wafers resulting in severe bending which is associated with both large bending angles and abrupt changes in lattice constants a and c.

A Fiber Bragg Grating–Based Inclinometer Fabricated Using 3-D Printing Method for Slope Monitoring

Abstract A new temperature-insensitive inclinometer was fabricated using a 3-D printing method based on fiber Bragg grating (FBG) sensors. This new tilt sensor is characterized by its light weight, immunity to electromagnetic interference (EMI) small size, quick prototyping, and cost effectiveness. FBG sensors were directly inscribed into polylactic acid, which was also used for fabricating all different parts of tilt sensors. Calibration tests of this new tilt sensor were performed in laboratory to examine its measurement performance. Measurement sensitivity of 0.012 nm/° and a maximum tilt angle of 25° of the FBG inclinometer was approached in the calibration experiment. The measured tilt angles were validated by theoretical angles calculated in terms of all physical parameters of internal functional parts of the inclinometer. A monitoring test of a sandy slope model using this new tilt sensor was conducted in laboratory. Finite element analysis was also used to examine the mechanical behavior of the slope model under different loading levels. Monitoring test results indicate that the FBG-based tilt sensor presented no obvious change before a surcharge load approaching 0.245 kN but exhibited step-by-step rise in tilt angle afterward, achieving a maximum tilt angle of around 6°. Horizontal displacement, which was calculated in terms of the tilt sensor at different loading levels, was found to agree fairly well with the displacement data from both finite element analysis and displacement transducers.

Experimental investigation of LNG release underwater and combustion behavior under crosswinds

Liquefied natural gas (LNG) trade has increased globally; therefore, assessments of the hazards of its accidental release and associated consequences must be conducted to ensure LNG security during marine transportation. This study aims to understand the dynamic behavior occurring when an LNG jet is released underwater and the combustion behavior of a flammable vapor cloud on the water’s surface with airflows from 0 to 4m/s. A series of controlled LNG vertical jet release experiments were conducted using a cryogenic storage tank with three orifices. Various instruments were employed to measure the flow rate and pressure in pipelines during different leakage scenarios, and the emanating LNG vapor clouds were immediately ignited with the mass loss rate of 0.016, 0.037, and 0.049kg/s in three orifices, respectively. The flame behavior was recorded by a video camera. With respect to flame length rapidly decreased with crosswinds of 0−2m/s and then gradually decreased to a constant value with the velocities increase to 4m/s. A dimensionless number of Ri was employed to analyze the relative magnitude between the buoyancy force and transverse flow. The flame tilt angle was found in accordance trend with flame length for first increased and further reach to become constant at Ri−1 increase to 2. As existing correlations provide an overestimation, a new correlation was established to describe the flame length as a function of crosswind speed, and a good prediction was found for measured tilt angles with the correlated values.

Elucidation of the de Vries behavior in terms of the orientational order parameter, apparent tilt angle, and field-induced tilt angle for smectic liquid crystals by polarized infrared spectroscopy.

We report experimental results of the orientational order parameter, the apparent tilt angle, and the field-induced tilt angle for three chiral smectic liquid crystalline materials investigated using infrared (IR) polarized spectroscopy. The common feature in these materials is use of the core 5-methyl-2- pyrimidine benzoate as the central part of the mesogen. This core is terminated by siloxane or carbosilane chains on one of the ends and by the chiral alkoxy chains on the opposite. These compounds exhibit low concomitant layer shrinkage at the smectic A^{*} (SmA^{*}) to smectic C^{*} (SmC^{*}) transition temperature and within the SmC^{*} phase itself. The maximum layer shrinkage in SmC^{*} is observed as ∼1.5%. We calculate the apparent orientational order parameter, S_{app} in the laboratory reference frame from the observed IR absorbance for homeotropic aligned samples, and the true order parameter, S, is calculated using the measured tilt angle and is also interpolated from Iso-SmA^{*} transition temperature closer to SmC^{*} phase. The apparent tilt angle in the SmA^{*} phase calculated from a comparison of order parameters S and S_{app} is found to be significantly large. A low magnitude of S_{app} found for homeotropic aligned samples in the SmA^{*} phase indicates that the order parameter plays a vital role in determining the de Vries characteristics, especially of exhibiting larger apparent tilt angles. Furthermore there is a significant increase in the true order parameter at temperatures close to SmA^{*} to SmC^{*} transition temperature in all three compounds. The planar-aligned samples are used to study the dependence of induced tilt angle on the applied electric field. The generalized Langevin-Debye model given by Shen etal. reasonably fits the experimental data on the field-induced tilt angle. The results show that the dipole moment of the tilt correlated domain in SmA^{*} diverges as temperature is lowered to the SmA^{*}-SmC^{*} transition temperature. The generalized Langevin-Debye model is also found to be extremely effective in confirming some of the conclusions of the de Vries behavior.

Acquisition Algorithm of Spatial Control Parameter Tilt Angle for On-line Insulator

Most vision control of the existing power-line insulator robot system needs to be realized indirectly through the remote computer. The vision system itself does not have the ability of vision control, and the level of automation is low. In order to improve the visual control ability and automation level of the power-line insulator robot, an on-line spatial control parameter acquisition algorithm for insulator is presented based on target extraction. The algorithm can be embedded in the hardware platform of visual system to automatically measure tilt angle of insulators. The results of hardware implementation show that the proposed algorithm can measure tilt angle parameters relatively accurately on the hardware platform of visual system. The error of tilt angle measurement is 0.4°~4°, which achieves the desired effect and design requirements.

Experimental study of dust deposition settled over tilted PV modules fixed in different directions in the southeast of Iran.

Degradation of photovoltaic system's power due to dust deposition is one of the important concerns of photovoltaic investors, especially the PV modules which are installed in the hot and dry parts of a country. This issue requires to be more understood and quantify its impact on the PV module performance in installation site. This study experimentally studied the dust deposition using several glasses which were fixed in the wooden frames at different tilt angles and directions in the southeast of Iran. The dust deposition on the glasses, solar energy reduction of the dusty glasses, and PV power reduction due to dust deposition were measured in all months of the year. The results showed that the average dust deposition on the glasses is 4.6 × 10-3 gr/m2day during the year. In case of no rain precipitation and no cleaning, this value reached 2.74 × 10-2gr/m2day. The percentage of solar energy reduction due to dust deposition was varied between 2 and 16% during the year. A correlation for prediction of the solar energy transmittance reduction based on the settled dust on the glass samples was developed in the studied region using 1-year data collection. The average solar energy reduction was obtained 7% during the year, and this value reached 44% in case of no rain precipitation and no glass cleaning. Results showed that in the most months of the year the wind direction and the direction of the glasses with the maximum dust deposition were coincided with each other. Furthermore, the experimental measurement showed that the calculated optimum monthly tilt angle in some months of the year is not the same with the measured tilt angle due to dust deposition. The difference between the calculated and measured tilt angles in these months was 15°.

On-Line Measurement of Dynamic Tilt Angle by Compensating Gyroscope Drift Error

In real-time movement controlling systems, it is essential to deploy a suitable sensor to measure tilt angle on-line. When the tilt angle is bigger than the preset threshold, the remedial operation should be made timely. This paper proposes an on-line dynamic tilt angle measurement method by compensating gyroscope drift error. First, gyroscope is selected as a measuring unit because it can overcome the interference of external forces to measure dynamic angular speed. Second, an improved least squares support vector machine (LSSVM) is proposed for gyroscope drift-error compensation. The vector base learning method is used to reduce those less important support vectors, and the sparsity of LSSVM can be changed by adjusting the value of $\theta $ . Third, the quantum-behaved particle swarm optimization algorithm is introduced as the optimization method to optimize regularization parameter C and kernel parameter $\gamma $ of LSSVM model because it has good optimization result and fast convergence speed. Fourth, the experiment platform and implementation process are illustrated in detail. Finally, the corresponding experimental results demonstrate that the proposed methodology could measure the dynamic tilt angle accurately.

An Approach to Measure Tilt Motion, Straightness and Position of Precision Linear Stage with a 3D Sinusoidal-Groove Linear Reflective Grating and Triangular Wave-Based Subdivision Method.

This work presents a novel and compact method for simultaneously measuring errors in linear displacement and vertical straightness of a moving linear air-bearing stage using 3D sinusoidal-groove linear reflective grating and a novel triangular wave-based sequence signal analysis method. The new scheme is distinct from the previous studies as it considers two signals to analyze linear displacement and vertical straightness. In addition, the tilt motion of the precision linear stage could also be measured using the 3D sinusoidal-groove linear reflective grating. The proposed system is similar to a linear encoder and can make online measurements of stage errors to analyze automatic processes and also be used for real-time monitoring. The performance of the proposed method and its reliability have been verified by experiments. The experiments show that the maximum error of measured tilt angle, linear displacement, and vertical straightness error is less than 0.058°, 0.239 μm, and 0.188 μm, respectively. The maximum repeatability error on measurement of tilt angle, linear displacement, and vertical straightness error is less than ±0.189o, ±0.093 μm, and ±0.016 μm, respectively. The proposed system is suitable for error compensation in the multi-axis system and finds application in most industries.

Electric-Field-Driven Molecular Recognition Reactions of Guanine with 1,2-Dipalmitoyl-sn-glycero-3-cytidine Monolayers Deposited on Gold Electrodes

Monolayers of 1,2-dipalmitoyl-sn-glycero-3-cytidine were incubated with guanine in a 0.1 M NaF electrolyte at the surface of a Langmuir trough and transferred to gold (111) electrodes using the Langmuir-Schaefer technique. Chronocoulometry and photon polarization modulation infrared reflection absorption spectroscopy were employed to investigate the influence of the static electric field on the orientation and conformation of the cytidine nucleolipid molecules on the metal surface in the presence of guanine and to monitor the molecular recognition of guanine with the cytosine moiety. When the monolayer is exposed to guanine solutions, the cytosine moiety binds to the guanine residue in either a Watson-Crick complex at positively charged electrode surfaces or a noncomplexed state at negative surface charges. The positive electrostatic field causes the cytosine moiety and the cytosine-guanine complex to adopt a nearly parallel orientation with respect to the plane of the monolayer with a measured tilt angle of ∼10°. The parallel orientation is stabilized by the interactions between the permanent dipole of the cytosine moiety or the Watson-Crick complex and the static electric field. At negative charge densities, the tilt of the cytosine moiety increases by ∼15-20°, destabilizing the complex. Our results demonstrate that the static electric field has an influence on the molecular recognition reactions between nucleoside base pairs at the metal-solution interface and can be controlled by altering the surface charge at the metal.

03:45 PM Abstract No. 194 Does lateral tilt during inferior vena cava filter placement result in subsequent need for advanced retrieval technique?

To investigate if lateral tilt during placement of an IVC filter is associated with lateral tilt during retrieval or need for advanced retrieval technique. Retrospective review of Gunther Tulip IVC filters placed and retrieved at our institution between 2015 and 2017 (n = 71) was performed after IRB approval. The angle between the filter and IVC was measured on pre-retrieval venogram (measured lateral tilt). Using the spinous processes of the adjacent vertebrae as an internal reference, calculated filter lateral tilt was then obtained by measuring the angle between the filter and spinous reference line (line connecting adjacent spinous processes) and the angle between IVC and spinous reference line. Intraclass correlation (ICC) analysis was performed using a two-way mixed effects ANOVA model to compare measured and calculated tilt demonstrating a high agreement between calculated and measured tilt angles (absolute ICC: 0.993, P<0.0001). Using this validated spinous process internal reference technique, the filter lateral tilt at time of placement was calculated using pre-placement venogram and intra-procedural post-placement spot radiograph. Filter retrievals were classified as standard (conventional snare) or advanced (technique other than conventional snare). Statistical analysis was performed using Stata for Mac v14.2. Dwell time-adjusted agreement between filter tilt angle at the time of placement and retrieval was fair (ICC coefficient = 0.57). Mean difference between tilt angle at the time of placement and retrieval was 4.4±4.2 degrees. A higher filter tilt angle during retrieval was significantly associated with advanced retrieval technique (P=0.026) while tilt angle during placement was not significantly associated with advanced retrieval technique (P=0.068). While higher lateral tilt of the Gunther Tulip filter measured at the time of retrieval is associated with the need for advanced retrieval technique, lateral tilt at the time of placement does not correlate with the need for advanced retrieval technique. Furthermore, lateral tilt at the time of placement is poorly associated with lateral tilt at the time of retrieval.

Pole tilt monitoring system using MEMs accelerometer and BeagleBone Black

Electric pole could tilt in the event of heavy storms, soil erosion and object crashing onto poles, causing serious damages if they are not fixed before condition worsen. Therefore, to monitor the health of the electric pole, a system to monitor its tilting angle is needed. In this paper, for the first time, to the best of our knowledge, an integration of Micro Electro-Mechanical Systems (MEMs) accelerometer with BeagleBone Black microcomputer will be used to develop an electric pole tile angle monitoring system. The accuracy of measuring tilt angle using single axis accelerometer versus triple axis accelerometer and the effect of rolling on tilt angle reading using single axis accelerometer versus triple axis accelerometer will be presented. Three-axis accelerometer achieves greater accuracy as the percentage error of tilting and rolling for the three-axis accelerometer are better than the single-axis accelerometer.

Molecular details of spontaneous insertion and interaction of HCV non-structure 3 protease protein domain with PIP2-containing membrane.

Hepatitis C virus (HCV), known as the leading cause of liver cirrhosis, viral hepatitis, and hepatocellular carcinoma, has been affecting more than 150 million people globally. The HCV non-structure 3 (NS3) protease protein domain plays a key role in HCV replication and pathogenesis; and is currently a primary target for HCV antiviral therapy. Through unbiased molecular dynamics simulations which take advantage of the novel highly mobile membrane mimetic model, we constructed the membrane-bound state of the protein domain at the atomic level. Our results indicated that protease domain of HCV NS3 protein can spontaneously bind and penetrate to an endoplasmic reticulum complex membrane containing phosphatidylinositol 4,5-bisphosphate (PIP2). An amphipathic helix α0 and loop S1 show their anchoring role to keep the protein on the membrane surface. Proper orientation of the protein domain at membrane surface was identified through measuring tilt angles of two specific vectors, wherein residue R161 plays a crucial role in its final orientation. Remarkably, PIP2 molecules were observed to bind to three main sites of the protease domain via specific electrostatic contacts and hydrogen bonds. PIP2-interaction determines the protein orientation at the membrane while both hydrophobic interplay and PIP2-interaction can stabilize the NS3 - membrane complex. Simulated results provide us with a detailed characterization of insertion, orientation and PIP2-interaction of NS3 protease domain at membrane environment, thus enhancing our understanding of structural functions and mechanism for the association of HCV non-structure 3 protein with respect to ER membranes.

A wireless tilt sensor based on plastic optical fiber and Arduino board microcontroller

In this paper, a tilt sensor based on Arduino board microcontroller and four plastic optical fibers which are orthogonally set up onto a pendulum for 2-D tilt measurement is presented. The pendulum structure is formed by suspending a heavy weight with a spring. When the sensor is sloped, the pendulum will stretch or bend plastic optical fibers to change the output power. From the intensity of the received illumination of each photoresistor and the digital conversion via Arduino microcontroller, we can obtain the azimuth and tilt angle of the inclined direction. The proposed sensor can be achieved of azimuth 0° to 360° measurement. And the measured tilt angle ranges from 0° to 15°. The resolution of the sensor is 1°. Furthermore, the conversion results of Arduino microcontrollers will be uploaded via Wi-Fi to the ThingSpeak platform. So, no matter personal computer, tablet or smartphone, all can real time monitor the result of the tilt of the test object by Internet.

Identifying the tilt angle and correcting the orbital angular momentum spectrum dispersion of misaligned light beam

The axis tilt of light beam in optical system would introduce the dispersion of orbital angular momentum (OAM) spectrum. To deal with it, a two-step method is proposed and demonstrated. First, the tilt angle of optical axis is identified with a deduced relation between the tilt angle and the variation of OAM topological charges with different reference axes, which is obtained with the help of a charge coupled device (CCD) camera. In our experiments, the precision of measured tilt angle is about 10−4rad with topological charges of −3~3. With the measured angle value, the additional phase delay due to axis tilt can be calculated so that the dispersion of OAM spectrum can be corrected with a simple formula while the optical axis is not aligned. The experimental results indicate that the original OAM spectrum has been successfully extracted for not only the pure state but also the superposed OAM states.