CN105241947A - Apparatus for generating low-temperature molecular beam and measuring speed and method - Google Patents

Abstract

The invention discloses an apparatus for generating a low-temperature molecular beam and measuring the speed and a method. The apparatus comprises a 4K low-temperature molecular beam source generator, an electrostatic quadrupolar direct guidance, a high-voltage direct-current power supply, a high-voltage switch, a DIO64 data acquisition card sequential control device, a LabVIEW control module and a quadrupolar mass spectrometer signal caliber. The method comprises enabling 4K temperature helium (He) atom to bump with a sample molecule to obtain a cold molecular beam, and fully bumping with 4K He atom, so as to obtain a molecular beam source with low translation and internal state temperature. The quadrupolar mass spectrometer detects all of molecules with stable chemical properties, and cooperates with the high-voltage switch and the electrostatic quadrupolar direct guidance, so that the speed distribution information of all of guidable polar molecules is obtained. The apparatus and the method are applicable to measure molecular beam speed distribution lack of molecular spectrum data information.

Description

The measurement mechanism of a kind of low temperature molecular beam generation and speed and method

Technical field

The present invention relates to cryovacuum technology field, be specifically related to a kind of 4K low temperature environment sample molecule and produce the method for low temperature molecular beam and the measuring method of velocity distribution by collision.

Background technology

At the eighties initial stage in last century, along with the maturation of laser-cooling technology, atomic physics has welcome its develop rapidly period.Atom cooling to below μ K, thus is achieved the Bose-Einstein condensation of atom by laser cooling, imprison and evaporative cooling.The laser of molecule cools and brings a new development opportunity to supercool physics.Slow down and cool the formation of ultra-cold molecules that obtains in precision measurement, supercool chemical reaction, the research of many scale of constructions subensemble and quantum information process has huge potential application.

But the cooling of molecule is a very challenging research topic, relative and atom, except having electronic state and nuclear spin state, molecule also has vibrational state and rotating state.In the complexity of molecule, state structure makes direct laser cool and becomes very difficult.But molecular physics does not need to be cooled to by molecule below μ K just can benefit from it, many physical phenomenons have started when a few K to manifest.In recent years in order to obtain low temperature molecular sample, people have developed different kinds of molecules bundle generation technology to produce the molecular beam source of precooling.These technology are mainly divided into following three kinds: a kind of is the method for ultrasonic molecular beam, the sample molecule of ratio very little (being generally less than 10%) and carrier gas from a high pressure (1-5 standard atmospheric pressure) container through a nozzle adiabatic expansion to high vacuum, in expansion process, intramolecule degree of freedom obtains effective cooling through multiple impacts.Because energy is converted into kinetic energy mostly, therefore the central speed of this molecular beam exceedes the velocity of sound usually.In molecular beam coordinate system, its velocity distribution width is very narrow, and use this technology can obtain translation temperature lower than 1K, rotational temperature is lower than the molecular beam of 5K.Another kind method is the method for jet beam, namely sample molecule directly from a high pressure vessel (1-100Pa) through nozzle adiabatic expansion to high vacuum, this method can produce the molecular beam that central speed is below 200m/s, but in the molecular beam that this method produces, state is not cooled, and molecular beam density is lower.Produce the advantage of cold molecular beam in conjunction with above two kinds, the third method producing cold molecular beam is arisen at the historic moment, i.e. buffer gas cooling.Buffer gas cooling is by fully colliding with low temperature He the cooling realizing sample molecule, this method can produce translation temperature and all very low low temperature cold molecular beam of interior state temperature, because the collision cross-section of buffer gas He and the energy of molecule and structure have nothing to do, therefore the method for the cold molecule of this preparation is applicable to the molecule of nearly all stable chemical nature.

The measuring method of molecular beam velocity distribution is mainly divided into following two kinds, and the first namely utilizes optical Doppler effect to carry out acquisition speed distributed intelligence by the method for spectrum.Principle is as follows: beat a branch of laser contrary with molecular beam direction of motion with another bundle perpendicular to the molecular beam direction of propagation respectively, determine the resonance absorption light frequency f of molecule after resonance absorption ₀and f, following relational expression can be obtained by optical Doppler effect: f ₀=f (1+v/c), its f ₀for the resonance absorption frequency of perpendicular molecules bundle direction of motion, f is the resonance absorption frequency contrary with molecular beam direction of motion, and v is the movement velocity of molecule, and c is the light velocity.Just can obtain the velocity profile information of molecular beam by this method.Second method obtains the time-of-flight mass spectrometry signal of molecular beam by the method for resonant multiphoton ionization and then obtains the velocity profile information of molecular beam.Owing to lacking spectroscopic data information, many molecules do not obtain the information of molecular beam by the method for optics.

Summary of the invention

The generation of a kind of low temperature molecular beam provided for the deficiencies in the prior art and velocity measuring device and method are provided, cooled by buffer gas and obtain low temperature molecular beam and directly utilize quadrupole mass spectroscope to carry out the measurement of molecular beam velocity distribution, to the molecule of stable chemical nature, there is universality.The velocity profile information that analyzing and processing obtains molecular beam is carried out by time-of-flight mass spectrometry (TOF) signal, simple and practical.

The object of the present invention is achieved like this:

A kind of generation of low temperature molecular beam and velocity measuring device, feature is: this device comprises: 4K low temperature molecular beam source generator, quiet electric quadrupole is directly guided, high-voltage DC power supply, high-voltage switch gear, DIO64 data collecting card time sequence control device, LabVIEW control module and quadrupole mass spectroscope signal measuring apparatus, described quiet electric quadrupole is directly guided and is connected 4K low temperature molecular beam source generator respectively, high-voltage DC power supply and high-voltage switch gear, DIO64 data collecting card time sequence control device connects high-voltage switch gear respectively, LabVIEW control module and quadrupole mass spectroscope signal measuring apparatus, LabVIEW control module connects quadrupole mass spectroscope signal measuring apparatus, wherein:

Described low temperature molecular beam generator comprises Cryo Refrigerator, copper chamber, constant temperature gas distribution pipeline and absorbent charcoal adsorber, and Cryo Refrigerator connects copper chamber and absorbent charcoal adsorber respectively, and copper chamber connects constant temperature gas distribution pipeline respectively and quiet electric quadrupole is directly guided;

Described quadrupole mass spectroscope signal measuring apparatus comprises quadrupole mass spectroscope main control cabinet, ion gun ionized region, radio frequency-ion screening field, signal deflection amplifier, secondary electron multiplier and MCS-32 data collecting card, quadrupole mass spectroscope main control cabinet, ion gun ionized region, radio frequency-ion screening field, signal deflection amplifier, secondary electron multiplier and MCS-32 data collecting card connect successively, and MCS-32 data collecting card connects DIO64 data collecting card time sequence control device and LabVIEW control module respectively.

Adopt said apparatus to implement the generation of low temperature molecular beam and a method for velocity survey, the method comprises the following steps:

Step one: open Cryo Refrigerator, under making low temperature molecular beam source generator be stabilized in the low temperature of 4K, passes into sample molecule gas and He atom makes it fully be collided in copper chamber;

Step 2: open quadrupole mass spectroscope measuring appliance carry out preheating half an hour go forward side by side line parameter arrange after open ion gun ionized region (11) filament and carry out molecular beam signal measurement;

Step 3: run LabVIEW control module, the square wave TTL signal of generation outputs to the switch of high-voltage switch gear and MCS-32 data collecting card synchro control steering voltage and the collection of signal data by DIO64 data collecting card time sequence control device thus obtains a time-of-flight mass spectrometry signal;

Step 4: the information that can be obtained signal intensity by the time-of-flight mass spectrometry signal obtained, carries out to the rising edge of TOF signal the velocity distribution that differential process obtains molecular beam;

The detailed process obtaining velocity distribution is as follows:

High-voltage switch gear is used for distinguishing signal and background, and when after unlatching high-voltage switch gear, being added in voltage that quiet electric quadrupole directly guides can ceaselessly repeat switch, and the cycle of repetition is 500ms, and switching time is respectively 200ms and 300ms; After high-voltage switch gear is opened, the fastest molecule of longitudinal velocity needs the ion gun ionized region through arriving quadrupole mass spectroscope after a period of time, thus the signal measured can rise, and this section of delay time correspond to the fastest molecule directly guides flight time at quiet electric quadrupole; The speed of molecular beam and the pass of flight time are:

t＝L/v

Wherein t is the time delays risen to signal after opening high-voltage switch gear, and L is the length that quiet electric quadrupole is directly guided, and v is the longitudinal velocity of molecule; Formula is above got differential to the time and can be obtained:

$\mathrm{\δ}t=-\frac{L}{v^2}\mathrm{\δ}v$

The speed molecule amount be between v to v+ δ v be δ t during this period of time in the increment of steering signal, be expressed as:

$f\left(v\right)\left(\mathrm{\δ}v\right)=-\frac{S(t+\mathrm{\δ}t)-S\left(t\right)}{\mathrm{\δ}t}\mathrm{\δ}t$

Wherein δ v is known quantity, the signal intensity that S (t) is t.The time-of-flight mass spectrometry signal measured by quadrupole mass spectroscope derives the velocity profile information of molecular beam.

Describedly pass into sample molecule gas and He atom is: sample molecule gas pipeline is heated by a constant temperature heating device makes temperature remain at more than the boiling point of sample molecule, the secondary cold head of He atom pipeline and Cryo Refrigerator has good thermo-contact, the He temperature passing into copper chamber is 4K, and the sample molecule gas temperature passed into is 300K; The amount passing into gas by two independently mass flowmeter control.

Beneficial effect of the present invention is: cooled by buffer gas and obtain low temperature molecular beam and directly utilize quadrupole mass spectroscope to carry out the method for molecular beam velocity distribution measurement, have universality to the molecule of stable chemical nature.The velocity profile information that analyzing and processing obtains molecular beam is carried out by time-of-flight mass spectrometry (TOF) signal, simple and practical.LabVIEW control module is powerful, both can be sent the TTL signal Control release signal synchronous collection of Control timing sequence by hardware alternately, can realize signal-obtaining and process again, and parameter adjustment is also convenient especially, uses flexibly.Can produce central speed is by this method 100m/s, and velocity distribution width is 65m/s, and signal intensity is 10 ¹¹the low temperature molecular beam of/s magnitude.

Accompanying drawing explanation

Fig. 1 is apparatus of the present invention structural representation;

Fig. 2 is that in apparatus of the present invention, 4K low temperature molecular beam source generator passes into 0.20SCCM helium (He), 2.00SCCM fluoromethane (CH ₃f) the mass signal figure of quadrupole mass spectroscope signal measuring apparatus (B) under sample molecule condition;

Fig. 3 is the CH that quadrupole mass spectroscope signal measuring apparatus of the present invention measurement obtains ₃time-of-flight mass spectrometry (TOF) signal data of F sample molecule;

Fig. 4 is for obtain CH by the process of LabVIEW control module ₃the velocity distribution data of F sample molecule, curve obtains by carrying out Gauss curve fitting to data, and error bar statistical procedures obtains.

Embodiment

Describe the present invention below in conjunction with accompanying drawing:

Consult Fig. 1, apparatus of the present invention comprise: 4K low temperature molecular beam source generator A, quiet electric quadrupole directly guides 5, high-voltage DC power supply 6, high-voltage switch gear 7, DIO64 data collecting card time sequence control device 8, LabVIEW control module 9 and quadrupole mass spectroscope signal measuring apparatus B, described quiet electric quadrupole is directly guided 5 and is connected 4K low temperature molecular beam source generator A respectively, high-voltage DC power supply 6 and high-voltage switch gear 7, DIO64 data collecting card time sequence control device 8 connects high-voltage switch gear 7 respectively, LabVIEW control module 9 and quadrupole mass spectroscope signal measuring apparatus B, LabVIEW control module 9 connects quadrupole mass spectroscope signal measuring apparatus B, wherein:

Described low temperature molecular beam generator A comprises Cryo Refrigerator 1, copper chamber 2, constant temperature gas distribution pipeline 3 and absorbent charcoal adsorber 4, Cryo Refrigerator 1 connects copper chamber 2 and absorbent charcoal adsorber 4 respectively, and copper chamber 2 connects constant temperature gas distribution pipeline 3 respectively and quiet electric quadrupole directly guides 5.

Described quadrupole mass spectroscope signal measuring apparatus B comprises quadrupole mass spectroscope main control cabinet 10, ion gun ionized region 11, radio frequency-ion screening field 12, signal deflection amplifier 13, secondary electron multiplier 14 and MCS-32 data collecting card 15, quadrupole mass spectroscope main control cabinet 10, ion gun ionized region 11, radio frequency-ion screening field 12, signal deflection amplifier 13, secondary electron multiplier 14 and MCS-32 data collecting card 15 connect successively, and MCS-32 data collecting card 15 connects DIO64 data collecting card time sequence control device 8 and LabVIEW control module 9 respectively.

The course of work of apparatus of the present invention: the sample molecule of room temperature and 4KHe atom are passed into low temperature copper chamber 2 by two different constant temperature gas distribution pipelines 3 and carried out sufficient cold collision rift inside copper chamber 2 and eject, the filtering that 5 carry out molecular beam transverse velocity is directly guided through quiet electric quadrupole, quiet electric quadrupole is directly guided 5 and is provided high direct voltage by DC high-voltage power supply 6, and carry out switch control rule accurately by high-voltage switch gear 7, DIO64 data collecting card time sequence control device 8 and MCS-32 data collecting card 15 control by LabVIEW control module 9, the output terminal of DIO64 data collecting card time sequence control device 8 is connected with the input end of high-voltage switch gear 7 and MCS-32 data collecting card 15 respectively, DIO64 data collecting card time sequence control device 8 controls the guiding of molecular beam and the collection of data, the TTL signal that LabVIEW control module 9 produces is input to the modulated terminal of high-voltage switch gear 7 by DIO64 data collecting card time sequence control device 8, realize carrying out switch modulation to being added in the voltage that quiet electric quadrupole directly guides 5, the TTL signal that LabVIEW control module 9 produces inputs MCS-32 data collecting card 15 by DIO64 data collecting card time sequence control device 8, realize deriving the synchronous selective of quadrupole mass spectroscope signal data, MCS-32 data collecting card 15 reads the sample molecule TOF signal that secondary electron multiplier 14 collects, the TOF signal of reading carries out processing thus obtains signal intensity and the velocity distribution of sample molecule bundle by LabVIEW control module 9.

Cryo Refrigerator 1 of the present invention can create the low temperature environment of a 4K, and copper chamber 2 and low temperature active charcoal adsorbent equipment 4 are contacted with it by good heat transfer material red copper and keep the steady temperature of 4K.Sample molecule pipeline makes temperature remain at more than the boiling point of sample molecule by a temperature controller, the secondary cold head of He pipeline and Cryo Refrigerator 1 has good thermo-contact, so the He temperature passing into copper chamber 2 is 4K, and the sample molecule temperature passed into is 300K.The amount passing into gas is controlled by mass flowmeter.

Because sample molecule is encountered above inwall will be adsorbed in the copper chamber 2 of 4K, He atom then can not, so its density in copper chamber 2 can be estimated according to the size in the He atom flow passed into and copper chamber 2.When in copper chamber 2, gas reaches balance, the He atom flow passed in copper chamber 2 equals the He atom flow exporting ejection from copper chamber 2, according to Thermodynamics Formulas: wherein f _outfor exporting the He atom flow of ejection from copper chamber 2, n _{0, b}the density of He atom in copper chamber 2 after balance, the average velocity of He atom at 4K temperature, A _aperturefor the aperture area that copper chamber 2 exports. therefore, the He atomic density n in copper chamber 2 _{0, b}can be expressed as:

$n_{0,b}=\frac{4f_{0,b}}{A_{aperture}{\stackrel{\‾}{v}}_{0,b}}$

The flow controlling to pass into He atom by mass flowmeter just accurately can control its density in copper chamber 2.The cooling of sample molecule is by completing with the collision of low temperature He atom.Because the density of sample molecule in copper chamber 2 is far below the density of He atom, therefore collide the density depending primarily on He atom.Collision process can be explained with the model of elastic pellet, and sample molecule and He atom collide through N time, and translation temperature TN can be expressed as:

T _N＝T _b+(T _i-T _b)e ^-(N/κ)

Wherein κ=(m _molecule+ m _helium) ²/ 2m _moleculem _heliumfor reduced mass, T _bthe temperature of He atom in copper chamber 2, T _ifor passing into copper chamber 2 sample molecule initial temperature.So just can estimate that passing into how many He atom just can make sample molecule fully be cooled.

In order to reduce ground unrest, extracting the He atom in background vacuum timely out, except keeping vacuum tightness with molecular pump, also on the radome in low temperature copper chamber 2, scribbling activated charcoal, in order to accelerate to absorb the He atom in background vacuum.Activated charcoal is a kind of organic material, and normally cocoanut shell carries out the moisture that heats to remove wherein, finally obtains porosint, such material has very large surface area to adsorb background gas, when 4K, test the pumping speed of activated charcoal, measuring method is as follows:

According to the end vacuum of vacuum plant and the relation of pumping speed: P _j=P ₀+ Q ₀/ S _p, wherein P _jfor the end vacuum that vacuum chamber can reach, P ₀for the end vacuum of vacuum pump, Q ₀during for zero load, the gas load of final vacuum room of bleeding for a long time, S _pfor the effective pumping speed of vacuum pump near vacuum chamber bleeding point.The permanent vacuum degree that vacuum chamber detects under room temperature after overbaking can reach P _j=8.9 × 10 ^-6pa, turbo-molecular pump type is Turbo-V1000HT, end vacuum P ₀=1.0 × 10 ^-8pa, effective pumping speed is S _p=1000L/s.Thus, the gas load Q in vacuum chamber can be obtained ₀=8.9 × 10 ^-3paL/s.After unlatching Cryo Refrigerator 1 makes activated charcoal reach 4K, the end vacuum of vacuum chamber can reach P _j=4.2 × 10 ^-8pa, instead can release the effective pumping speed S of the low temperature active charcoal under 4K in vacuum chamber thus _p=2.1 × 10 ⁵l/s.These parameters demonstrate activated charcoal under cryogenic can as the cryopump of super large pumping speed, and its pumping speed is far longer than the molecular pump of Mechanics of Machinery design.

The mainframe box 10 of quadrupole mass spectroscope of the present invention is for controlling the work of quadrupole mass spectroscope various piece, the molecular beam produced by low temperature molecular beam generator A arrives ion gun ionized region 11 through quadrupole rod electrostatic guide and is ionized by filament, selection through radio frequency-ion screening field 12 through 90 degree of deflections of signal deflection amplifier 13, then carry out signal amplification through secondary electron multiplier 14, the signal after amplification to read and stored in computer through MCS-32 data collecting card 15.Fig. 2 passes into 0.20SCCMHe, 2.00SCCMCH ₃the mass signal of F sample molecule.

LabVIEW control module 9 of the present invention produces two-way TTL signal by DIO64 data collecting card time sequence control device 8, a-road-through enters the adjustable input end of high-voltage switch gear 7, a-road-through enters the adjustable input control end of data acquisition of MCS-32 data collecting card 15 in addition, the reading of signal measured by the loading of synchro control positive or negative high voltage and mass spectrometer.The signal read is stored in computer, and signal obtains the velocity distribution of cold molecular beam through LabVIEW control module 9 process.Concrete implementation step is as follows:

Step one: open Cryo Refrigerator, under low temperature molecular beam source generating device can be stabilized in the low temperature of 4K after a period of time, the sample molecule gas and the He that pass into certain flow make it fully be collided in copper chamber.

Step 2: directly guide to add high pressure and open quadrupole mass spectroscope measurement mechanism to quiet electric quadrupole and carry out preheating, carries out optimum configurations unlatching filament and carries out molecular beam signal measurement after preheated.

Step 3: run LabVIEW program, the square wave TTL signal of generation outputs to the switch of high-voltage switch gear and MCS-32 data collecting card synchro control steering voltage and the collection of signal data by DIO64 data collecting card thus obtains a time-of-flight mass spectrometry signal.

Step 4: the rising edge LabVIEW of the time-of-flight mass spectrometry signal obtained is carried out the velocity distribution that differential process obtains molecular beam.

Consult Fig. 3, Fig. 3 display be molecular beam TOF signal after the high-voltage switch gear work obtained under adding the condition of positive and negative 4kV high pressure.Consider that four pole electrostatic bar guiding efficiency and quadrupole mass spectroscope measure efficiency, can 10 be obtained ¹¹the low temperature molecular beam of/s magnitude.

Consult Fig. 4, Fig. 4 display be through the sample molecule velocity distribution that LabVIEW data processing obtains, matched curve is obtained by Gauss curve fitting, and error bar is obtained by statistical errors process.By controlling suitable flowrate proportioning, can obtain central speed is 100m/s, and velocity distribution width is the cryogenic sample molecular beam of 65m/s.

Claims (2)

1. the measurement mechanism of a low temperature molecular beam generation and speed, it is characterized in that, this device comprises: 4K low temperature molecular beam source generator (A), quiet electric quadrupole is directly guided (5), high-voltage DC power supply (6), high-voltage switch gear (7), DIO64 data collecting card time sequence control device (8), LabVIEW control module (9) and quadrupole mass spectroscope signal measuring apparatus (B), described quiet electric quadrupole is directly guided (5) and is connected 4K low temperature molecular beam source generator (A) respectively, high-voltage DC power supply (6) and high-voltage switch gear (7), DIO64 data collecting card time sequence control device (8) connects high-voltage switch gear (7) respectively, LabVIEW control module (9) and quadrupole mass spectroscope signal measuring apparatus (B), LabVIEW control module (9) connects quadrupole mass spectroscope signal measuring apparatus (B), wherein:

Described low temperature molecular beam generator (A) comprises Cryo Refrigerator (1), copper chamber (2), constant temperature gas distribution pipeline (3) and absorbent charcoal adsorber (4), Cryo Refrigerator (1) connects copper chamber (2) and absorbent charcoal adsorber (4) respectively, and copper chamber (2) connect constant temperature gas distribution pipeline (3) respectively and quiet electric quadrupole is directly guided (5);

Described quadrupole mass spectroscope signal measuring apparatus (B) comprises quadrupole mass spectroscope main control cabinet (10), ion gun ionized region (11), radio frequency-ion screening field (12), signal deflection amplifier (13), secondary electron multiplier (14) and MCS-32 data collecting card (15), quadrupole mass spectroscope main control cabinet (10), ion gun ionized region (11), radio frequency-ion screening field (12), signal deflection amplifier (13), secondary electron multiplier (14) and MCS-32 data collecting card (15) connect successively, MCS-32 data collecting card (15) connects DIO64 data collecting card time sequence control device (8) and LabVIEW control module (9) respectively.

2. adopt device described in claim 1 to implement a measuring method for low temperature molecular beam generation and speed, it is characterized in that, the method comprises the following steps:

Step one: open Cryo Refrigerator (1), under making low temperature molecular beam source generator (A) be stabilized in the low temperature of 4K, passes into sample molecule gas and He atom and makes it fully be collided copper chamber (2) are inner;

Step 2: open quadrupole mass spectroscope measuring appliance (B) carry out preheating half an hour go forward side by side line parameter arrange after open ion gun ionized region (11) filament and carry out molecular beam signal measurement;

Step 3: run LabVIEW control module (9), the square wave TTL signal of generation outputs to the switch of high-voltage switch gear (7) and MCS-32 data collecting card (15) synchro control steering voltage and the collection of signal data by DIO64 data collecting card time sequence control device (8) thus obtains a time-of-flight mass spectrometry signal;

Step 4: the information that can be obtained signal intensity by the time-of-flight mass spectrometry signal obtained, carries out to the rising edge of TOF signal the velocity distribution that differential process obtains molecular beam;

The detailed process obtaining velocity distribution is as follows:

High-voltage switch gear (7) is used for distinguishing signal and background, when after unlatching high-voltage switch gear (7), be added in quiet electric quadrupole directly guide the voltage of (5) can ceaselessly repeat switch, the cycle of repetition is 500ms, and switching time is respectively 200ms and 300ms.After high-voltage switch gear is opened, the fastest molecule of longitudinal velocity needs the ion gun ionized region through arriving quadrupole mass spectroscope after a period of time, thus the signal measured can rise, and this section of delay time correspond to the fastest molecule directly guides the time of (5) flying at quiet electric quadrupole; The speed of molecular beam and the pass of flight time are:

t＝L/v

Wherein t is the time delays risen to signal after opening high-voltage switch gear, and L is the length that quiet electric quadrupole is directly guided, and v is the longitudinal velocity of molecule; Formula is above got differential to the time and can be obtained:

$\mathrm{\δ}t=-\frac{L}{v^2}\mathrm{\δ}v$

The speed molecule amount be between v to v+ δ v be δ t during this period of time in the increment of steering signal, be expressed as:

$f\left(v\right)\left(\mathrm{\δ}v\right)=-\frac{S(t+\mathrm{\δ}t)-S\left(t\right)}{\mathrm{\δ}t}\mathrm{\δ}t$

Wherein δ v is known quantity, the signal intensity that S (t) is t; The time-of-flight mass spectrometry signal measured by quadrupole mass spectroscope derives the velocity profile information of molecular beam.