methods for calibrating stopwatch

Calibration of Stopwatch by Using High Speed Video Recording

and an In-house Designed Synchronous Counter

Speaker: C.M.TsuiThe Government of the Hong Kong Special Administrative Region

Standards and Calibration Laboratory36/F Immigration Tower, 7 Gloucester Road, Wanchai, Hong Kong

Phone: (852) 2829 4850, Fax: (852) 2824 1302, Email: [email protected]: C.M.Tsui, Y.K.Yan, H.M. Chan

The Government of the Hong Kong Special Administrative RegionStandards and Calibration Laboratory

mailto:[email protected]

Methods for Calibrating Stopwatch

Stopwatch can be calibrated using three methods :

The direct comparison methodThe totalize methodThe time base method The time base method has the smallest measurement uncertainty. The direct comparison method has the largest.

The Direct Comparison Method

The time interval measured by the stopwatch is compared to that of a traceable time interval reference which usually is an audio signal broadcast by the official timekeeper of a region. An example is the WWVH in the USA.

The Time Base Method

The frequency of the time base of the stopwatch, which is likely to be a quartz oscillator, is pickup by either ultrasonic acoustic sensor or inductive sensor and measured directly.

This method is very fast. The measurement can be completed in a few seconds.

Since only the time base is tested, the functionality of the stopwatch is not checked. In addition, the relationship between the time interval readings of the stopwatch and its time base is not known.

The Totalize Method

A laboratory time interval reference is set up as follows.

At beginning of measurement, the stopwatch is started and the universal counter’s gate is opened at the same time. After some time, the stopwatch is stopped and the counter’s gate closed.

The time interval measured by the stopwatch and the counter is compared.

Traceable frequency standard

Signal generator

Universal counter

Photo Totalize Method (1)

A high speed camera is used to take photo of the stopwatch and a universal counter when they are both counting. After a suitable time has elapsed, another photo is taken.

Traceable frequency standard

Signal generator

Universal counter

Stopwatch

Camera

Photo Totalize Method (2)

The elapsed time measured by the stopwatch and the universal counter can then be obtained from these two photos and compared. The relative correction is

The measurement uncertainty is dependent upon the display resolution of the stopwatch.

8120.511 8119.4counter stopwatch

Photo 2

2.567 1.3counter stopwatch

Photo 1

51092.1)567.2511.8120(

)3.14.8119()567.2511.8120(

Video Totalize Method (1)

We has modified this method by utilizing video recordings instead of photographs to obtain readings of the stopwatch.

The instant when the reading of the stopwatch display changes is found by examining the recorded video frame-by-frame.

The measurement uncertainty is limited by the

frame rate of the video recording rather than the display resolution of the stopwatch.

Video Totalize Method (2)

Digital cameras that can record high speed video at 240 fps or 420 fps are commercially available. Using such cameras, the measurement uncertainty can be reduced significantly.

At high frame rates, the display of a normal universal counter cannot keep up and does not update at uniform intervals.

To overcome these problems, we has designed and built a synchronous counter that allows its count to be easily read from a recorded video with a resolution as small as 1 millisecond

SCL Caesium Beam Frequency Standard

Signal Generator

LSD Indicator

1

2

3

45

7

8

9

6

0

Stopwatch under test

1 kHz Clock dicator

High Speed Video Camera

10 MHz Reference Clock

In-house Designed Synchronous Counter

Figure 1

A signal generator feeds a 1 kHz clock signal to the synchronous counter. This 1 kHz clock is phase locked with the laboratory caesium frequency standard.

A high speed digital camera CASIO EX-FH100 is used to record a 10 second video clip at 240 fps or 420 fps for the stopwatch and the synchronous counter when they are both counting.

The Calibration Method

The recorded video is viewed frame-by-frame to search for a frame at which the display of the stopwatch starts to change to a new value.

The readings of the stopwatch Tuut_start and that for the synchronous counter Tref_start are then taken from the frame immediately preceding this frame.

The least-significant-digit (LSD) of the synchronous counter is indicated by a circular LED display. The value corresponds to the LED which lights up at the most clockwise position.

Synchronous counter reading is 442.069s. (442.06 from the 7-segment LED display. The most clockwise LED that lights up in the circular indicator is “9”, hence the LSD is 9) The reading of the digital watch is 11:09:54

Synchronous counter reading is 442.073 s. The LSD of the digital watch reading starts to change from “4” to “5”. The lowest segment of the digit “5” is noticeable in this picture. If this is chosen as the start time of measurement, then Tuut_start = 11:09:54 and Tref_start = 442.069 s (i.e. the last frame)Figure

2(a)

The synchronous counter reading is 442.077 s. The digital watch reading is changing from 11:09:54 to 11:09:55. The change is obvious in this picture.

The reading of the synchronous counter is 442.081 s. The reading of the digital watch is changing from 11:09:54 to 11:09:55.

Figure 2(b)

The synchronous counter reading is

852.180 s. The reading of the UUT

is 00:02:00. The second hand has

remained stationery at this position for over

20 frames.

The synchronous counter reading is

852.185 s. It can be seen that the second hand of

the stopwatch has moved a little bit.

Figure 3(a)

Figure 3(b)

The Calibration Method

After a suitable time interval (say 6 or 7 hours), the above process is repeated to obtain Tuut_stop and Tref_stop. The relative correction is defined as

standard laboratoryby reported elapsed Time

UUTbyreported elapsed Timestandardlaboratoryby reported elapsed TimeCorrection Relative

)(

) ()(Correction Relative

ref_startref_stop

uut_startuut_stopref_startref_stop

TTTTTT

High Speed Digital Camera (1)

A high speed digital camera CASIO EX-FH100 is used to record video. It supports the following high speed video modes.

Frame rate Image size (pixels)120 fps 640 x 480240 fps 448 x 336420 fps 224 x 1681000 fps 224 x 64

High Speed Digital Camera (2)

The image size for the 1000 fps mode is too small. The shutter speed for the 120 fps mode was too slow (~10 ms)

The 420 fps mode is suitable if the stopwatch has a large and clear display. Otherwise the 240 fps mode is recommended.

At high frame rate, more light is required due to higher shutter speed. The video should be captured in a well-lit environment.

In-house Designed Synchronous Counter (1)

The display readings of many commercial universal counters did not update synchronously with the input clock signal.

In Figure 4, the time between frames is about 2.38 ms. If the display of the universal counter was truly synchronous, the counter reading should increment by 2 or 3 with each new frame.

However, we can only observe three readings during this 76.2 ms period: 11490, 11539 and 11588. The universal counter seems to only update its display about once every 49 ms

Progress of frame sequence

Figure 4. Display of a commercial universal counter captured by a high speed digital camera at 420 fps. The universal counter is driven by a 1 kHz clock input.

There are severe limitations when the video totalize method is employed with some commercial universal counters.

The synchronous counter designed by SCL was built with logic circuits that ensure its 10-digit LED display will be updated synchronously with the input clock.

It is driven by a 1 kHz clock generated by a signal generator phase locked to the laboratory cesium frequency standard. It has a resolution of 1 ms.


Figure 5

At 420 fps and 240 fps, the shutter speeds were 2 ms and 4 ms respectively. The LSD of the counter updates every millisecond, it is not possible to read its value from the 7-segment LED display in the recorded video.

To overcome this problem, a special LSD indicator was designed which consists of 10 LED arranged in a circle. Each LED corresponds to a decimal value and will light up individually for about 1 ms in every 10 ms period.

When recorded at a shutter speed of 4 ms, 4 to 5 consecutive LEDs will be illuminated in the recorded image. The LED which lights up at the most clockwise position is the correct value of the LSD, and allows the counter to be read with a resolution of 1 ms.


VCC

VCC

1514

3

5

4

9 10 1211 13

16

8

2 617

VCC

GND

DA DB DC DD

Og OfLT

BI

EL

Oe Od Oc Ob Oa

74HC4511B

7-segment display

17 18 1 2 3 15 16

14

VCC

8

16

15

1 12 111314

9

2

5 6

7

10

43

VCC

RCO

QA QB QC QDCLR

GNDCLK

EN T

LD A B C D

EN P74HC162

VCC

To ResetButton

Fromlowerdigit

To higherdigit

1 kHzClock

Figure 6. Simplified circuit diagram for a single digit of the synchronous counter.

To ResetButton

1 kHzClock

VCC

VCC

74LS138

16

8

Vcc

GND

2 3 4 5 6

74LS138

E1A0

1

A1 A2

7915 1011121314

16

8

Vcc

GND

E3E2

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

VCC

8

16

15

1 12 111314

9

2

5 6

7

10

43

VCC

RCO

QA QB QC QDCLR

GNDCLK

EN T

LD A B C D

EN P74HC162

VCC

VCC

To higherdigit

7915 1011121314

Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7

2 3 4 5 6

E1A0

1

A1 A2 E3E2

Figure 7. Circuit diagram for the least-significant-digit (LSD) indicator.

Measurement Uncertainty Evaluation

The measurement model for the relative correction (RC) of elapsed time counting of a stopwatch is shown below.

)(C)(1

) ()(C)(1RC

ref_startref_stop

uut_startuut_stopref_startref_stop

TTTTTT


Measurement Uncertainty Components

Remarks

C Relative correction of the 1 kHz clock input to the synchronous counter

The 1 kHz clock input is phase locked to the laboratory reference frequency. It is assumed to have a normal distribution with zero mean. The standard measurement uncertainty is taken as :

Tref_start , Tref_stop

Reading of synchronous counter at start and stop time of elapsed time counting.

Due to limited resolution of the synchronous counter. It is taken to have a rectangular distribution with semi-range of ± 1 ms.

Tuut_start , Tuut_stop

Reading of UUT at start and stop time of elapsed time counting.

Due to time interval between successive frames of the video recording. It is taken to have a rectangular distribution with semi-range equals to the time interval between two frames.

)TT(864005104)C(

ref_startref_stop

14

u


There are two methods to derive the combined standard measurement uncertainty for the final measurand GUM Uncertainty Framework (GUF) Monte Carlo Method (MCM)

GUF is easier and faster to compute than MCM. However, the domain of validity of GUF is narrower than MCM.

Supplement 1 to the GUM describes a validation procedure for GUF. GUF was found not valid for this measurement model.

The reason is that there are two dominant uncertainty components u(Tuut_start) and u(Tuut_stop) with rectangular probability distribution, violating the condition for valid application of GUF.


Assuming elapsed time of 7 hours between Tref_start and Tref_stop, the estimated measurement uncertainties of the relative correction RC for a 95% coverage interval, calculated using MCM, are listed on next slide.

For comparison, the estimated measurement uncertainties for the photo totalise method are listed in the same table. If commercial counter is used in the photo totalise method, the counter reading taken from the photo is assumed to have an accuracy of 0.1 s.


Display resolution of stopwatch under test

Estimated measurement uncertainty of the relative correction RC for a 95% coverage interval

Video totalize method used Photo totalize method used

Video recording at

240 fps

Video recording at

420 fps

Using the synchronous

counter described in this paper

Using commercial

counter

1 s 2.7 x 10-7 1.6 x 10-7 3.1 x 10-5 3.2 x 10-5

0.1 s 2.7 x 10-7 1.6 x 10-7 3.1 x 10-6 7.0 x 10-6

0.01 s 2.7 x 10-7 1.6 x 10-7 3.2 x 10-7 6.2 x 10-6

methods for calibrating stopwatch

Documents