Copyright: VideoCom by Leybold Didactic GmbH, 1997
Citation: VideoCom by Leybold Didactic GmbH, 1997


Introduction Motions
VideoCom Motions

Introduction

Measuring

Evaluation

Experiment notes

VideoCom registers the positions of one or more reflections of retroreflecting tape via a CCD (charge-coupled device). The LED flash screwed onto the camera lens ensures sufficient contrast. The detected positions of the retroreflecting tape strips (and thus the corresponding bodies) are displayed directly on the display instrument in the form of a corresponding number of pointers. The display instrument comprises two parts (top: analog, bottom: digital). When more than one analog pointer is present, the digital display can be switched by clicking on the desired pointer.

The speed buttons at the top of the window let you access the basic functions of the software directly, making it easier to use. The most important speed buttons are also mapped to function keys.

Below the button bar, you can change the representation of the display instrument, table and diagram by clicking on the tabs. When Path is active, paths are displayed; the same applies for Velocity, Acceleration, Formula, Newton, Fourier analysis and Intensity Test. Path, velocity, acceleration and the quantities determined using the formula can be displayed in any combination, even all at once, using Select View (right mouse button).

The display instrument, table and diagram can be enlarged or reduced with respect to each other by moving the boundaries with the mouse.

The display instrument and the diagram of velocities and accelerations can also be scaled manually using the corresponding buttons at the left and right edge of the display instrument (see screen shot).

You can select your evaluation options using the right mouse button.

F4

Clears either the current measurement while retaining the settings or, when no measurement is displayed, the current settings.

Pressing this key twice clears the current measurement with all settings.

Before you can start a new measurement you must first clear the old one, unless you want to compare the two measurement series.

F3

Opens a measurement series with its settings and its evaluations.

The measurement series can be opened in addition to an existing one (but without loading its calibrations and evaluations) to allow you to compare different measurements.

F2

Saves the current measurement series with its settings and its evaluations.

You can also save just the settings (without measurement data) to make it easier to repeat an experiment at a later date. In this case, only a new path calibration (possibly with linearization) is required.

Prints out the current diagram.

F9

Starts and stops a new measurement.

Alternatively, you can use the MODE and START/STOP keys on VideoCom or start and stop the measurement by entering a parameter for the measuring time or measuring path.

F5

Changes the current settings (e.g. time interval, measuring time, linearization, path calibration, formula, Newton’s equation of motion, serial interface).

F6

Toggles a large display of the status-line information on and off.

F1

Opens this help file.

Indicates the software version.


Intensity Test

This test is only provided for „troubleshooting“ your setups. 256 representative intensity values of the CCD are displayed. A position is always registered when a reflection achieves an intensity of about 15%. If too many positions are registered, the VideoCom aperture is probably not at the minimum f-stop, or the background is too bright (e.g. backlighting). If to few positions are registered, VideoCom is probably not aligned precisely enough, the LED flash is not screwed on or the flash is not set to automatic.

VideoCom is not affected by bare metal parts in its field of view, as long as these reflect no light to VideoCom. If such reflections should occur (e.g. from the rail of the air track), you can remedy this by changing the height of VideoCom, and thus the angle of incidence of the light flashes.


Status line

Evaluation results always appear in the status line at the bottom of the window. You can toggle display of this information in a larger window on and off by pressing [image] or F6.


Measuring Motions
Measuring

In determining the position of a body, the positions of the left and right edges of a reflection on the CCD (2048 pixels) are added together; the result is a number between approx. 0 and 4000 for each position. When a reflection is detected, its position is displayed in the display instrument Path. This measure of position can be calibrated and subsequently converted to the true position automatically.

F9

Starts and stops a new measurement. Alternatively, you can use the MODE and START/STOP keys on VideoCom or start and stop the measurement by entering a parameter for the measuring time or measuring path.

The measured values are entered in the table and displayed in the diagram while the measurement is running. If these already contain old measurements, the new measured values are added to the table and the diagram. This permits direct comparison of multiple measurements (e.g. for confirming Newton’s equation of motion).

Clicking the right mouse button opens the evaluation menu.


Settings/Path Calibration

This dialog box allows you to make the most important settings. These are divided into six tabs:

Measuring Parameters (VideoCom settings and preselection of measuring stop)

Linearization (correction of imaging distortions)

Path Calibration (calibration of pixel information in paths s in m)

Formula (calculation of quantities from the measurement quantities s, v, a and t)

Newton (settings for confirming the equation of motion)

General (selection of serial interface and saving of program parameters)

Shortcut

Keyboard:	F5


Setting the measuring parameters

You can vary the time interval Δt between two measurements in steps between 12.5 ms (80 frames/s) and 200 ms (5 frames/s). The exposure time of the camera remains constant at 1.25 ms. However, you can set the flash to determine for how much of this time the LEDs are to flash. The default automatic exposure ensures that the CCD is not overdriven, and should not be altered in normal operation.

Smoothing refers to a method by which the velocities and accelerations are calculated. By default, a symmetric derivation of the type

v(i) = ( s(i+2) - s(i-2) ) / 4Δt

is used. A change in smoothing affects all previously recorded values.

The measurement can be stopped either with the START/STOP key or automatically after a predefined time or path.

Remark

For a registered path of 1 m, VideoCom resolves Δs =0.25 mm in path measurement. This good but finite resolution for Δs means that v and a also have a finite resolution, which additionally depends on the time interval Δt and the selected smoothing. For the given default smoothing, Δt=12.5 ms results in Δv=0.005 m/s and Δa=0.1 m/s². In particular, this can make itself apparent in a by producing spikes in the measuring curve. Better resolution can be obtained using a higher smoothing value or a greater time interval. In both cases, the averaging time for calculation of velocities and accelerations is increased.


Linearization

When the VideoCom CCD is not positioned parallel to the motion, the image of the motion on the CCD is no longer linear (see drawing). Lens imaging aberrations (cushion or barrel distortions) also cause non-linear imaging.

Normally, these errors are negligible. It is only in precision measurements (e.g. free fall) that correcting these errors is worth while. Such errors occur most often in the a(t)-diagram at high velocities (e.g. gravitational acceleration at the end of the measuring path is no longer constant). In principle, there are two ways to correct such errors:

Either enter the angle α between VideoCom and the motion and/or the distortion δ of the lens manually, or let the software suggest two values. To arrive at a suggestion, however, the system must already have recorded a measurement series having two positions s1 and s2 with a constant path difference s2-s1=constant. To do this, you can e.g. allow the falling body for VideoCom (337 472) fall or attach two strips of reflecting tape to a slider and move it along the track once. The calculated suggestion optimizes the measured difference s2-s1 to the most constant possible value.

Attention

Linearization may alter the previously defined path calibration. This must then be repeated (e.g. using the function Read Pixels from Table).

Hints

The drawing above applies for positive angles of α. The linearization can be used to adjust the angle α by turning VideoCom correspondingly after calculating the current angle α. Of course, this is only necessary when no subsequent angle correction is to be carried out.

Once you have determined the distortion of the lens, you can manually enter it as an approximate value for later measurements.

The difference s2-s1 can be calculated using a formula. The effectiveness of linearization is thus easy to observe.


Path Calibration

VideoCom can only determine the position of one reflection on the CCD. This position is a number (or pixel coordinate) between 0 and about 4000. Assuming a linear image on the CCD, two points are sufficient for converting these positions into real paths.

Calibration is easiest when two positions in the display are measured simultaneously or s1 and s2 already exist in the table. The measured pixel coordinates can then be read directly using Read Pixels from Display or Read Pixels from Table. The corresponding real positions s in m must then be taken from the real experiment conditions and entered.

If only one position is measured at a time, Read Pixels from Display transfers the first pixel coordinate the first time, and the second pixel coordinate the second time. Do not exit the calibration box during this process.

To cancel a calibration, deactivate the check box Apply Calibration. The software again shows pixel coordinates instead of the paths calibrated with them.

If necessary, you can change the order of positions (and thus the sign of the velocity) with Invert Positions.


Formula settings

Depending on t, s, v and a, you can use this page to define any number of formulas to calculate the measurement quantities which are then displayed in the diagram as a function of the time t. You must give the formula a name, which subsequently appears in selecting the view. The symbol and unit subsequently serve as the label for the corresponding table column and the y-axis of the diagram. The specified minimum and maximum define the scale for the display instrument and the diagram.

Typical examples of valid formulas include:

s1+s2	; decoupled oscillation of two coupled pendulums

0.5*0.1*v1^2	; kinetic energy in Nm for a mass of 0.1 kg

0.2*a1	; force in N for a mass of 0.2 kg

Hints

The formulas can contain a comment when the latter is preceded by a semicolon.

The formulas can also be displayed in addition to an existing s(t), v(t) or a(t) diagram using Select View. In the selected overview, the respective scalings of the y-axes are independent of each other, and are thus usually not directly comparable in quantitative terms.

To directly, quantitatively compare a formula with a measurement quantity (e.g. for a comparison with theory), the measurement quantity must be entered as a second formula (e.g. s1) in addition to the theoretical formula (e.g. 0.5*9.81*t^2).


Newton settings

As VideoCom cannot measure the quantities force F and mass m required to confirm Newton’s equation of motion F=ma, one of these two quantities must be varied while the other is maintained constant; VideoCom then determines the respective acceleration a.

Depending on which parameter is selected as the variable, either F or m appears next to a in the initially empty table of measured values for Newton and a blank F(a), m(a) or m(1/a)-diagram is displayed. Each click of the left mouse button expands the table by one line. The active input field is always surrounded by a broken line. You can read the acceleration values from the v(t) or a(t) diagrams of the measurement by fitting a straight line or determining the mean value.

Evaluation

The slope of the best-fit straight line of an F(a) diagram gives us the constantly accelerated mass m. It is important that the accelerated mass m was truly constant during the measurement, and especially that the different accelerating forces were not produced by adding additional weights to the system, but only by transferring weights between the driven mass (trolley) and the driving mass.

The slope of the best-fit straight line of the m(1/a) diagram resp. the coefficient of the best-fit hyperbola of an m(a) diagram provides the constant accelerating force F.

Hint

You do not need to note the numerical value of acceleration when you activate the acceleration input box directly after evaluation (mean value in a(t)-diagram or best-fit straight line in v(t)-diagram) and start the input cursor with a second mouse click. You can then transfer the last numerical value with Ctrl + V.


General settings

This page lets you change the language and the serial interface at which VideoCom is connected to the computer. Changeover takes effect immediately - you do not need to exit the dialog box with OK, so that you can check your changes immediately.

If you want to save your changes so that you can have them ready the next time you use the software, you additionally need to select Save New Parameters. This will also save the current settings of the graph display at the same time:

Display Coordinates

Select Line Width

Show Values

Show Connecting Lines

Select Rulers

Show Color Spectrum

Show Grid

The identification code designates the device and the version information of the VideoCom camera. If the version of the software implemented in the camera is newer or older than this software, a message is generated. Selecting Update VideoCom causes this software to overwrite the software implemented in the camera (regardless of whether it is newer or older).

Hint

If this software is older than VideoCom or you wish to update your software, you can download the latest version from our website: http://www.leybold-didactic.de.


Experiment notes

Motions on a track

Elastic collision

Free fall

Coupled pendulums

Generally speaking, VideoCom is ideal for all one-dimensional linear motions in which a strip of retroreflecting tape can be attached to the body in motion (e.g. track, collision, free fall, bar pendulum). In this case, the LED flash screwed onto the camera lens ensures sufficient contrast for recording measured values.

Normally, you do not need to change the settings of the camera lens (minimum aperture, focus on infinity).

VideoCom must be aligned so that the CCD can register the entire motion of the body or bodies. This camera adjustment is easiest when a trolley with retroreflecting tape is positioned at each end of the motion, and the alignment and distance of VideoCom is varied until both reflections are reliably recognized. The spirit level on the side is very useful when aligning for free-fall experiments.

The default time interval Δt of the measurement is 100 ms. In free fall or collision, this value should be reduced to 12.5 ms.

A path calibration must be carried out to enable conversion of pixel information into the position of the experiment body (best carried out before the measurement, but still possible afterwards).

An additional linearization is only seldom required.

Note

If problems arise in registering position, use the Intensity Test.

Mechanics with VideoCom in Leybold Physics Leaflets

P1.3.3.7	Recording path-time diagrams of linear motions (planned)

P1.3.3.8	Uniformly accelerated motion with reversal of direction (planned)

P1.3.3.9	Kinetic energy of a uniformly accelerated mass (planned)

P1.3.4.4	Laws of collision (planned)

P1.3.5.4	Free fall (planned)

P1.5.4.2	Coupled pendulums (planned)


Motions on a track

Set up VideoCom at a suitable distance (around twice the length of the track) and parallel to the track. Subsequent adjustment of the setup is easiest when a reflector (retroreflecting tape) is attached to the left and right ends of the track. Both reflections must be indicated on the VideoCom LCD. If you are having problems, try increasing the distance and/or changing the alignment of the camera.

Δt=100 ms is normally a sufficient time interval. Measurement stop is either manual at keystroke or automatically after a predefined time or path.

For path calibration it is then only necessary to specify the real paths in m for the displayed pixel positions (Read Pixels from Display). If you need to linearize the measurement to increase accuracy, you must first conduct a test measurement with two reflectors on the same trolley. The trolley must travel the entire track during the measurement. From the measured (not constant) distance between the two reflectors, the software can calculate the required corrections for further measurements.

As it is possible to record any number of measurement series one after another and compare them in a common diagram, confirming Newton’s equation of motion (with variable force or variable mass) is an ideal application for VideoCom. The expected result is the proportionality between F and a or the inverse proportionality between m and a.


Elastic collision

Adjust and calibrate VideoCom as described for a motion on a track. However, as this interesting motion process occurs extremely rapidly (compression and extension of springs during collision), VideoCom must be set to the time interval Δt=12.5 ms to enable observation. Using heavy trolleys is also recommended to prolong the duration of the collision.

In addition to the s(t), v(t) and a(t) diagrams, which are particularly interesting during collision, you can of course use formulas to measure and evaluate this phenomenon.

m1*v1+m2*v2	; shows the linear momentum p as a function of the time (enter m1 and m2 as numerical values)

m1*a1	; shows the force F1 acting on the first trolley (enter m1 as numerical value)

m2*a2	; shows the force F2 acting on the second trolley (enter m2 as numerical value)

In the first case, the conservation of momentum is derived from the constancy of the calculated quantity (even during collision). The use of the latter two formulas impressively confirms Newton’s third law (action = reaction) from which the law of conservation of momentum can be derived in turn (the transfer of force = momentum is determined through integration). VideoCom can thus be used as a contact-free two-channel dynamometer whenever F1=m1*a1 and F2=m2*a2 can be displayed directly during measurement.


Free fall

To record free fall, set up VideoCom vertically (spirit level up). The falling body for VideoCom (337 472) is suspended from a holding magnet (336 21) at a suitable distance. The holding-magnet voltage, which can be adjusted at VideoCom, should be set to the lowest possible level to ensure that the start of motion and measurement are as nearly simultaneous as possible. Both reflections of the falling body must be must be reliably indicated at the top end of the VideoCom LCD. To register the fall, use a time interval Δt=12.5 ms.

The distance d=0.2 m of the two detected reflections can be easily used for path calibration. Note that the first (bottom) reflection corresponds to position s1=0.2 m and the second (top) reflection to position s2=0 m. Due to the double reflection, two s(t), v(t) and a(t) diagrams are produced after the measurement. As only s2 passes through the origin, s1 can now be deleted (place the right mouse button on the corresponding table column).

However, precision free-fall measurements also require linearization of the image. The measurement with two reflections can be used for this as well, as the linearization can be calculated from the inconstancy of the measured distance s1-s2. Note that the setup must be calibrated again after linearizing. You can take care of this after the measurement just by selecting Read Pixels from Table.

Linearization after measurement is not necessary when VideoCom is exactly vertical and a previously determined lens imaging distortion has already been entered before the measurement.

VideoCom can record measured values for free fall so exactly that even the slight effects of air friction can be recognized. Thus, the deviation of a second experiment from the first can be illustrated easily by directly comparing the diagrams. In particular, the acceleration of the falling body is no longer constant when air resistance is increased (e.g. by attaching two small wings).


Coupled pendulums

After calibrating by assigning the two real pendulum positions to the displayed pixel positions, you can start the measurement. A suitable time interval is Δt=100 ms. This scanning rate of f=10 Hz subsequently results in Fourier analysis in the end value f/2=5 Hz.

In addition to the s(t), v(t) and a(t) diagrams, which are particularly interesting during the phase shift, you can also use formulas to evaluate the experiment

s1+s2	; displays one fundamental oscillation

s1-s2	; displays the other fundamental oscillation

Assuming optimum starting conditions, these two formulas decoupled the coupled oscillation. The two decoupled oscillations have different oscillation frequencies (fundamental frequencies). You can also determine their envelopes.

Additionally, you can determine the fundamental frequencies directly using Fourier analysis.

As VideoCom can follow more than two pendulums, you can of course expand the experiment to include multiple fundamental oscillations and frequencies.


Introduction Intensities
VideoCom Intensities

Introduction

Measuring

Evaluation

Experiment notes

VideoCom registers the intensities of 2048 pixels of a CCD (charge-coupled device). The intensity distribution to be studied is imaged on the CCD. If necessary, you can demount the camera lens. The LED flash is not used for these intensity measurements.

The speed buttons at the top of the window let you access the basic functions of the software directly, making it easier to use. The most important speed buttons are also mapped to function keys.

Below the button bar, you can change the representation of the display instrument, table and diagram by clicking on the tabs. When Intensity I1 is active, the intensities measured by the CCD are displayed. The same applies for Reference I2, except that the intensities are entered in table column I2. In Transmission T=I1/I2, I1 is measured and immediately divided by reference I2. The resulting ratio T=I1/I2 is displayed. Finally, Theory enables a quantitative comparison with theory for interference curves which result from diffraction at a slit, grating or half-plane (edge).

The table and diagram can be enlarged or reduced with respect to each other by moving the boundaries with the mouse.

You can select your evaluation options using the right mouse button.

F4

Clears either the current measurement while retaining the calibration or, when no measurement is displayed, the current calibration.

Pressing this key twice clears the current measurement with all settings.

F3

Opens a measurement series with its calibration and its evaluations, and simultaneously clears any previously existing measurement series.

F2

Saves the current measurement series with its calibration and its evaluations.

Prints out the current diagram.

F8, F9

Starts and stops a measurement with the resolutions 256 or 2048 pixels.

Alternatively, you can use the MODE and START/STOP keys on VideoCom.

F5

Changes the current calibration (diffraction angle, wavelength) as well as comparison with theory and serial interface.

F6

Toggles a large display of the status-line information on and off.

F1

Opens this help file.

Indicates the software version.


Measuring Intensities
Measuring

In intensity measurement, the light intensities registered by the individual CCD pixels are converted to numerical values between 0 and 250 and then into percentage brightness values between 0 and 100 %.

F8, F9

Starts and stops a measurement with a resolution of either 256 or 2048 pixels. Alternatively, you can use the MODE and START/STOP keys on VideoCom.

The measured values are entered in the table and displayed in the diagram while the measurement is running. For Intensity I1, Transmission T and Theory, table column I1 is updated and T=I1/I2 is recalculated as needed. For Reference I2, column I2 is updated. In the theoretical display, an adjustable theoretical intensity distribution is also displayed.

When working at low resolution (256 pixels), a measured value is only inserted in every eighth table row. Transmission values are only calculated when the reference intensity is at least 15 %. Otherwise, the corresponding table values are blank.

Clicking the right mouse button opens the evaluation menu.


Calibration/Comparison with Theory

This dialog box allows you to make the most important settings. These are divided into four tabs:

Diffraction Angle Calibration (calibration of pixel information in diffraction angles α)

Wavelength Calibration (calibration of diffraction angles α in wavelengths λ)

Theory (comparison of current measurement with theory)

General (selection of serial interface and saving of program parameters)

Shortcut

Keyboard:	F5


Diffraction Angle Calibration

To begin with, the current measurement can be corrected if necessary by subtracting a background level which is caused by external light. You can also execute this operation automatically using Background at Minimum.

Before you can carry out a comparison with theory or a wavelength calibration, the individual pixels of the CCD must be assigned to a diffraction angle α. For this to be possible, you must specify the effective focal length f with which the diffraction angle can be calculated to

α = arctan (x/f)

 (x=(1024-p)*14 µm with p = pixel coordinate on the CCD from 0 to 2047). In all experiments which generate a diffraction pattern on the CCD (e.g. single slit, multiple slit, grating and grating spectroscopy), f is the focal length of the lens (or lens system) used. The VideoCom lens alone has a focal length of f = 50 mm.

Examples

If a diffraction pattern is imaged directly on the CCD (without camera lens) behind a slit with an optics lens f = 500 mm, then the effective focal length is equal to 500 mm. If no lens at all is used (e.g. for diffraction at a half-plane), the distance between the diffraction object and the CCD must be entered in order to enable calculation of the diffraction angle.

Normally, the optical axis of the experiment setup will not fall precisely on the middle of the CCD (α=0°). This can be compensated by shifting the zero point α=0°. The button Zero Point Corresponds to Maximum automatically shifts the zero point to the maximum of the intensity distribution (e.g. for diffraction at a slit). This zero-point shift is calculated and executed in the subsequent wavelength calibration.


Wavelength Calibration

For grating spectroscopy, calibration in diffraction angles alone is not sufficient. However, you can use the diffraction angle α to determine the wavelength λ with the formula

λ = sin α / nD

when the diffraction order n and the grating constant D (here in lines per mm) are known.

Important

The wavelength calibration is extremely sensitive to the sign of the diffraction order n. When the spectrum is reversed left to right (i.e. red at left and blue at right), change the sign of the diffraction order n. You can recognize inversion of the spectrum e.g. after a test measurement with a red filter.

Finally, the spectrum must be shifted. When you enter a shift in nm, the software calculates the corresponding zero-point shift of the diffraction angle calibration. This zero-point shift assumes small angles α and may thus need to be carried out a second time.

Alternatively, you can also calibrate the wavelength by entering two diffraction angles with their corresponding wavelengths. The function Suggest Calibration then calculates the appropriate grating constant D, the sign of the diffraction order n and the corresponding shift. In principle, this calibration with two known wavelengths is more precise than the above method with only one wavelength (shift).

Remark

The lines of a mercury spectrum are well suited for calibration. Using a suitable setup, it is possible to recognize four particularly intensive lines (indicated with *). Of the characteristic ultraviolet lines, we can recognize at best just the line with λ=366 nm, as most of the ultraviolet radiation is absorbed by the lenses and the glass window of the CCD.

red	690 nm

yellow	578 nm*

green	546 nm*

blue-green	492 nm

blue	436 nm*

violet	406 nm*

ultraviolet	366 nm


Comparison with Theory

A comparison with theory is only possible when the measurement has already been calculated in diffraction angles. The software provides a choice of three configurations:

Slit

Grating

Half-plane

The data required for calculating the theoretical values of each measurement can be entered manually. Only the maximum amplitude, required for slit and grating, can be automatically determined from the current measurement using Automatic Maximum and then automatically entered.

Remark

Close agreement with theory is only possible when monochromatic light (e.g. a beam of broadened laser light) falls on a diffraction object in parallel. For the slit and the grating the diffraction pattern must be imaged on the CCD (e.g. with a lens f = 500 mm).

For the half-plane the shadow range of the theoretical distribution lies at negative angles α and the brightness range in positive angles α. If this is inverted in the measuring curve, you can reverse the angular assignment by entering a negative effective focal length (distance between half-plane and CCD).

Formulas

Slit:

λ: wavelength, b: slit width, α: diffraction angle

Grating:

λ: wavelength, b: slit width, N : number of slits, d: slit spacing, α: diffraction angle

Half-plane:

λ: wavelength, f: distance between CCD and half-plane, x: position on the CCD


Experiment notes

Diffraction at a slit, multiple slit and grating

Diffraction at a half-plane

Grating spectroscopy

Generally speaking, VideoCom can be used to register intensity distributions which can feasibly be imaged on the 20 mm long CCD line (e.g. diffraction at a slit, a grating and a half-plane, grating spectroscopy).

To obtain satisfactory experiment results, you must make sure to adjust the axis of the optical arrangement carefully, starting with the light source (left side) and VideoCom (right side). The light source (e.g. laser) and VideoCom should be aligned so that both units lie precisely on the optical axis. Then set up the remaining components working from left to right, always taking care not to disturb the optical axis. You also need to make sure that the beam path is as parallel as possible in front of the diffraction object.

Note

VideoCom only measures the intensities of a line. Light which passes through the lens diagonally upward or downward does not fall on the CCD line.

Optics with VideoCom in LEYBOLD Physics Leaflets

P5.3.1.6	Diffraction at a single slit (planned)

P5.3.1.7	Diffraction at a double slit and multiple slits (planned)

P5.3.1.8	Diffraction at a half-plane (planned)

P5.7.2.2	Assembling a grating spectrometer for measuring transmission curves (planned)


Diffraction at a slit, multiple slit and grating

A broadened beam of parallel, linearly polarized laser light (e.g. from 471 840) falls on the diffraction object (slit, multiple slit or grating). Behind the diffraction object, a lens (e.g. f = 500 mm) produces a sharp image of the diffraction pattern on the CCD. You will need to demount the VideoCom lens for this experiment. The polarization filter in the beam path serves to set the intensity.

For diffraction angle calibration, you need to specify the focal length of the imaging lens. Any shift of the angle zero point can be carried out automatically according to the visible maximum of the diffraction pattern. After entering the wavelength of the laser used, the slit width, the maximum intensity and, where applicable, the number of slits and the slit spacing, you can compare your measured intensity distribution with the distribution to be expected according to theory.

Interference phenomena

The coherent laser light passes through several lenses as well as the protective glass pane of the CCD before falling on the light-sensitive layer of the CCD. Each glass element can cause interference. Therefore, you cannot expect the intensity distribution of the undiffracted laser light to show a smooth curve. Interference artifacts are apparent in the diffracted laser light as well (spikes up to about 5 % of the measured intensity).


Diffraction at a half-plane (edge)

A broadened beam of parallel, linearly polarized laser light (e.g. from 471 840) falls on the diffraction object (half-plane, e.g. calling card, razor blade). The light falls directly on the CCD (without optics lenses or camera lens). The polarization filter in the beam path serves to set the intensity.

The actual measurement of diffraction at the half-plane is conducted in two steps. First, the Reference distribution is measured without the half-plane. Then the Transmission of the half-plane can be determined in comparison to the reference measurement without half-plane. The distance between half-plane and CCD is entered for diffraction angle calibration. Any required zero-point shift must be executed manually. The angle α=0° corresponds to a transmission of 25 %. After entering the wavelength of the laser used, you can compare your measured transmission curve with the distribution to be expected according to theory.

The shadow range of the theoretical distribution falls in negative angles α and the brightness range in positive angles α. If this is inverted in the actual measuring curve, you can reverse the angular assignment by entering a negative effective focal length (distance between half-plane and CCD).

Important

Reference intensities less than 15 % are not taken into account when calculating transmission. Accordingly, if an important range of the calculated transmission curve is missing, you need to increase the intensity over this range.

Interference phenomena

The coherent laser light passes through several lenses as well as the protective glass pane of the CCD before falling on the light-sensitive layer of the CCD. Each glass element can cause interference. Therefore, you cannot expect the intensity distribution of the undiffracted laser light to show a smooth curve. However, as each diffracted distribution is divided by the corresponding undiffracted distribution, these interference phenomena no longer play an important role in the transmission curve.


Grating spectroscopy (filter transmission curves)

The light from an incandescent light bulb is imaged on a slit. Behind the slit, a lens is set up at a suitable distance so that parallel light falls on a grating (e.g. 600 lines/mm). VideoCom, with attached lens, is set up behind the grating as closely as possible, so that the first diffraction order is visible. To adjust the intensity, you can vary either the slit width or the aperture of the camera lens.

For diffraction angle calibration, the focal length of the lens (50 mm) is entered. Wavelength calibration is achieved using the grating constant (600 lines/mm) and a wavelength shift. You can easily determine the necessary shift of the spectrum using a known filter. If the spectrum is reversed left to right (i.e. red at left and blue at right), change the sign of the diffraction order n. In the drawing above, the sign of the diffraction order n is given.

Remarks

Alternatively, you can calibrate the wavelength by entering two diffraction angles with their corresponding wavelengths (e.g. for two known lines of a high-pressure mercury vapor lamp).

To better utilize the full length of the CCD, you can place a telescope (e.g. with f = 300 mm and f = 150 mm) between the grating and VideoCom. In the example described here, the resulting effective focal length is f = -100 mm (negative for left-right inversion). However, the quality of the grating spectrometer suffers somewhat from the fact that the focal lengths of the two lenses are wavelength-dependent and the effective focal length is thus not constant.

Interference phenomena

When the setup has been adjusted precisely, coherent light with a slightly different wavelength falls on each pixel of the CCD. The CCD is coated with a thin layer, at which this light interferes through double reflection (interference at thin layers). This becomes apparent in the wavelike structure which occurs in the spectral sensitivity of the CCD.

Filter transmission

When measuring filter transmission curves, however, these interference phenomena no longer play a significant role, as each filtered distribution is divided by the corresponding unfiltered distribution. First, measure the unfiltered distribution as the Reference. The Transmission display then shows the ratio of the current measured intensity distribution (e.g. with a filter between lamp and slit) to the reference distribution. You can make the evaluation even more visually interesting by activating the function Show Color Spectrum for wavelengths between 400 nm and 800 nm.

Important

Transmission calculation omits all reference intensities which are lower than 15 %. Accordingly, if an important range of the calculated transmission curve (e.g. blue) is missing, you need to increase the intensity over this range. You can obtain e.g. a greater blue component (in comparison to the red component) by increasing the lamp voltage.

Depending on the stability of the local mains voltage, an unregulated lamp power supply (e.g. via a transformer) may cause visible fluctuations in the reference. The only solution for this is to use a stabilized power supply (e.g. 521 55).


Marking a curve section

In some cases, you may wish to mark a particular curve section for which the evaluation is to perform a calculation.

To do this, move the pointer to the starting point of the curve section and hold down the left mouse button; then drag the pointer to the end of the curve section and release the mouse button. Alternatively, you can also click on the starting and end points.

During marking, the marked curve section is displayed in green.


Evaluations

You can access a wide variety of powerful evaluation functions by clicking the right mouse button

Select View

Delete Column

Display Coordinates

Select Line Width

Show Values

Show Connecting Lines

Select Rulers

Show Color Spectrum

Show Grid

Zoom

Zoom Off

Set Marker

Text

Vertical Line

Horizontal Line

Measure Difference

Draw Mean Value

Fit Function

Calculate Integral

Calculate FFT

Shortcut for accessing this help file

Keyboard:	F1 for help on the active menu command when the popup menu is activated.

Select View (VideoCom Motions only)

The view selection determines which curves (s, v, a or formula) appear simultaneously in the table and the diagram.

The y-axis of the diagram (switchable with one of the tabs above the display instrument) is then always with reference to the black curve or to the colored curve set. The other curves are shown in gray, and generally have a different y-ruler than the colored curves. Quantitative comparison is thus not possible. Instead, quantitative comparison can be carried out using two formulas.

Delete Column (VideoCom Motions only)

Deletes the table column which is under the mouse pointer at the time the right mouse button is pressed.

If one of the columns s, v or a is deleted, then the two other columns belonging to it are deleted as well. Deletion of a formula column simultaneously deletes the corresponding formula. The time, the frequency and the intensities of the Intensity Test cannot be deleted.

Display Coordinates

When you activate this function, the status line shows the current coordinates of the mouse pointer, as long as it is over a diagram. The coordinate display remains active until you deactivate this menu point by selecting it again, or one of the evaluations Set Marker, Draw Mean Value, Fit Function or Calculate Integral shows a result in the status line.

You can also display the current coordinates in the diagram. However, make sure that you access the menu point Text via the keyboard with Alt+T without changing the coordinates of the mouse pointer, as otherwise the wrong coordinates would be loaded.

You can save the current setting as the parameter for further program starts in General.

Shortcut

Keyboard:	Alt + C

Select Line Width

You can modify the line width for display of the diagrams and the evaluations which you carry out in them. You can choose between thin, medium and thick lines.

You can save the current setting as the parameter for further program starts in General.

Show Values (VideoCom Motions only)

The function Show Values shows the positions of the individual measured values as small squares.

You can save the current setting as the parameter for further program starts in General.

Show Connecting Lines (VideoCom Motions only)

Use this function to toggle the connecting lines between measurement points on and off.

You can save the current setting as the parameter for further program starts in General.

Select Rulers

This function sets display of rulers at top and left, at bottom and left or off.

You can save the current setting as the parameter for further program starts in General.

Show Color Spectrum (VideoCom Intensities only)

When the x-axis is already calibrated in wavelengths, you can toggle a color spectrum under the measuring curve for the wavelengths between 400 nm and 800 nm which corresponds to the displayed wavelengths. A color resolution of at least 65,536 colors is recommended.

You can save the current setting as the parameter for further program starts in General.

Show Grid

Allows you to toggle a grid on and off in each diagram.

You can save the current setting as the parameter for further program starts in General.

Zoom

Once you activate the zoom function with this menu point, you need to mark the range you wish to enlarge by holding down the left mouse button and dragging the mouse pointer.

A zoomed range can be zoomed even further, or reset using Zoom Off.

Shortcut

Keyboard:	Alt + Z

Zoom Off

Returns the currently selected section of the diagram to its original size.

Shortcut

Keyboard:	Alt + O

Set Marker

This software provides four different mark-up functions.

You can edit the markers, move them or delete them from the diagram by double-clicking on them with the left mouse button.

Alt+T:	Text

This text function lets you label all parts of the diagram using any text you wish to enter. Once you have entered your text, just move it to the desired position and anchor it with the left mouse button.

After all evaluations which return a numerical value in the status line, these numerical values are suggested as a text insertion; you can accept, edit or reject these suggestions.

Alt+V:	Vertical Line

This function lets you draw vertical lines in any positions in the diagram. The respective position is given in the status line. If the status line contains a coordinate display this is switched off.

Alt+H:	Horizontal Line

This function lets you draw horizontal lines in any positions in the diagram. The respective position is given in the status line. If the status line contains a coordinate display this is switched off.

Alt+D:	Measure Difference

After clicking on a reference point, you can draw a line to any point in the diagram. The coordinate difference between the starting and end points of that line are given in the status line. If the status line contains a coordinate display this is switched off.

Draw Mean Value (VideoCom Motions only)

After choosing mean value calculation, just select the curve section for which you wish to find the mean value with the left mouse button. The mean value appears in the status line along with its statistical error. If the status line contains a coordinate display this is switched off.

You can also insert the mean value in the diagram as Text.

The mean-value line can be deleted from the diagram again by double-clicking on it.

Fit Functions (VideoCom Motions only)

The software offers a choice of five best-fit operations:

Best-Fit Straight Line	y=Ax+B

Line through Origin	y=Ax

Parabola	y=Ax²+Bx+C

Hyperbola	y=A/x+B

Envelope of an Oscillation	y=±A*exp(-x/B)+C	(attenuation through air friction)

After choosing the corresponding operation, select the curve section  you wish to apply it to using the left mouse button.

During the fit, the current parameters of the operation (A, B and C) appear in the status line. If the status line contains a coordinate display this is switched off. You can also insert these values in the diagram as Text..

The operation can be deleted from the diagram again by double-clicking on it.

Calculate Integral (VideoCom Motions only)

The value of the integral is determined from the area bounded by the curve section you select with the left mouse button and the x-axis. The value of the integral appears in the status line. If the status line contains a coordinate display this is switched off.

You can also insert the current value of the integral in the diagram as Text.

Calculate FFT (Fourier window) (VideoCom Motions only)

This function enables you to apply Fourier analysis to a selected curve section. The result is displayed in an A(f)-diagram. The maximum of the amplitude is normalized at 100 % each time.

Delete Last Evaluation

Undoes the most recent evaluation operation. This is possible for the following evaluation functions.

Set Marker

Draw Mean Value (VideoCom Motions only)

Fit Function (VideoCom Motions only)

Calculate Integral (VideoCom Motions only)

Shortcut

Keyboard:	Alt + Backspace

Delete All Evaluations

Undoes all evaluation operations. This applies for the following evaluations:

Set Marker

Draw Mean Value (VideoCom Motions only)

Fit Function (VideoCom Motions only)

Calculate Integral (VideoCom Motions only)


Clipboard

The functions Copy Table, Copy Diagram and Copy Window let you copy the table in text format, the diagram or the main window as bitmap to the Windows clipboard, where it can be imported into other Windows programs.