Patent Publication Number: US-2009225014-A1

Title: Control of semiconductor light emitting element

Description:
BACKGROUND OF THE INVENTION 
     The entire disclosure of Japanese Patent Application No. 2008-056036, filed Mar. 6, 2008 and is expressly incorporated herein by reference. 
     1. Technical Field 
     The present invention relates to a semiconductor light emitting element. More specifically, the present invention relates to a system and method for controlling a semiconductor light emitting element. 
     2. Related Art 
     Projectors have traditionally used high-pressure mercury lamps as light sources. More recently, semiconductor lasers have been used as a projector light source. For example, Japanese Publication No. JP-A-2000-294871 and U.S. Pat. No. 6,243,407 each describe examples of projectors which use semiconductor lasers as a light source. 
     When a semiconductor laser is used as the light source, the intensity or emission amount of light emitted from the semiconductor laser can be varied due to heat generation even when the input value sent to the semiconductor laser remains constant. In this case, the image displayed by the projector can be different from the image represented by the image data. This phenomenon becomes even more prominent in, for example, situations where the semiconductor laser uses the thermal lens effect. 
     It should be noted this problem occurs not only in semiconductor lasers but also in other semiconductor light emitting elements such as light emitting diodes. Further, the problem described above is not limited to the projectors, but common to the light source devices which include semiconductor light emitting elements. 
     BRIEF SUMMARY OF THE INVENTION 
     An advantage of some aspects of the invention is to make the semiconductor light emitting element emit the light having intensity corresponding to the input value accurately. 
     Systems and methods of the invention are directed to a light source device including a semiconductor light emitting element, and a control section adapted to control the semiconductor light emitting element in accordance with an input value which includes a characteristic value calculation section adapted to calculate a characteristic value representing an input-output characteristic of the semiconductor light emitting element in accordance with a measurement value related to the semiconductor light emitting element, a current supply section adapted to supply the semiconductor light emitting element with a drive current based on the characteristic value, the input value, and an estimation value of a threshold current of the semiconductor light emitting element, and an estimation section adapted to obtain the estimation value of the threshold current used in the current supply section, using a value of the drive current, a light amount detection value related to an amount of light emitted from the semiconductor light emitting element, and the characteristic value. 
     In the light source device described herein, a characteristic value representing the characteristic of the semiconductor light emitting element and the estimation value of the threshold current are obtained. A drive current corresponding thereto is supplied to the semiconductor light emitting element even when the characteristic thereof varies in accordance with the temperature of the light source device. Therefore, even in the case in which the characteristic of the semiconductor light emitting element varies due to the temperature variation, it becomes possible to accurately emit light from the semiconductor light emitting element with the intensity corresponding to the input value. 
     It should be noted that the invention can be put into practice in various forms such as a light source device including a semiconductor light emitting element, control device and method for a semiconductor light emitting element, an image display device equipped with a light source device, control device and method for the image display device, a computer program for realizing the function of the method or the device, a recording medium storing the computer program, or a data signal including the computer program and realized in a carrier wave. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the accompanying drawings, wherein like numbers reference like elements. 
         FIG. 1  is an explanatory diagram showing a schematic configuration of a projector; 
         FIGS. 2A and 2B  are explanatory diagrams schematically showing a method of operating the projector of  FIG. 1 ; 
         FIGS. 3A-3E  are timing charts showing the operation of a light source device as currently performed in the art; 
         FIG. 4  is an explanatory diagram showing a schematic configuration of a light source device; 
         FIGS. 5A-5C  are explanatory diagrams illustrating the function of a differential efficiency adjustment section; 
         FIG. 6  is an explanatory diagram showing an internal configuration of a current driver; 
         FIGS. 7A-7E  are timing charts showing a method of operating a light source device; 
         FIG. 8  is an explanatory diagram showing a specific configuration of a light source device; 
         FIG. 9  is an explanatory diagram showing a circuit diagram of a light source device; 
         FIG. 10  is an explanatory diagram showing a circuit diagram of a light source device; 
         FIG. 11  is a block diagram showing a schematic configuration of a differential efficiency adjustment section; 
         FIGS. 12A-12D  are explanatory diagrams showing schematic configurations of an operation section of the differential efficiency adjustment section; 
         FIG. 13  is an explanatory diagram showing a circuit diagram of the differential efficiency adjustment section; 
         FIGS. 14A and 14B  are explanatory diagrams illustrating another example of the method of calculating an integration value of a product of a light amount error and a grayscale value; and 
         FIG. 15  is an explanatory diagram showing another example of the circuit diagram of the differential efficiency adjustment section. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Some embodiments of the invention will hereinafter be explained based on some specific examples in the following order.
     A. Embodiments
       A-1. Configuration of Projector   A-2. Comparative Example   A-3. Configuration of Light Source Device   A-4. Operation of Light Source Device   A-5. Threshold Current Estimator   A-6. Differential Efficiency Adjustment Section   
       B. Modified Examples   

     A. EMBODIMENTS 
     A-1. CONFIGURATION OF PROJECTOR 
       FIG. 1  is an explanatory diagram showing a schematic configuration of a projector PJ. The projector PJ is a so-called raster scanning type rear projector. The projector PJ is provided with a light source device  50 , a polygon mirror  62 , a mirror drive section  64 , and a screen  70 . 
     The light source device  50  is provided with a semiconductor laser which emits a laser beam from the light source device  50 . Specifically, the light source device  50  emits light at an intensity which corresponds to pixel data (pixel values) in order to form the image data. The polygon mirror  62  includes a plurality of mirror surfaces, and each of the mirror surfaces reflects the light emitted from the light source device  50  towards the screen  70 . The mirror drive section  64  rotates the polygon mirror  62  around the center axis C in the counterclockwise direction. Therefore, the light formed on the screen  70  is scanned on the screen  70  in the X-direction. Further, the mirror drive section  64  turns the polygon mirror  62  around an axis which is parallel to the X-direction. Therefore, the scan line of the spot of the light moves gradually in a Y direction. The screen  70  is a diffusing plate, and diffuses the incident light. As a result, the image represented by the image data is displayed on the screen  70 . It should be noted that the observer observes the image using the afterimage phenomenon. 
       FIGS. 2A and 2B  are explanatory diagrams schematically showing the operation of the projector PJ.  FIG. 2A  shows the rotational angle of the polygon mirror  62 , and the lower part and  FIG. 2B  shows the intensity or emission amount of light emitted from the light source device  50 . 
     The rotational angle of the polygon mirror  62  shown in  FIG. 2A  represents the rotational angle of the object mirror surface to which the light emitted from the light source device  50  is input. A base period Ta represents the period during which the laser beam enters the object mirror surface, assuming that the laser beam is constantly emitted from the light source device  50 . The starting point of the base period Ta corresponds to the minimum value (min) of the rotational angle of the object mirror surface, and the end point of the base period Ta corresponds to the maximum value (max) of the rotational angle of the object mirror surface. In the present embodiment, as shown in  FIG. 2B , the light source device  50  emits light only in an effective period Tb, which is only a portion of the base period Ta. Therefore, only a partial image or line image corresponding to one scan line is drawn when the rotational angle of the object mirror surface is increased in the effective period Tb. It should be noted that the period T 0  shown in  FIG. 2B  will be more fully below. 
     Incidentally, in the raster scanning type projector PJ described above, the intensity of the light emitted from the light source device  50  preferably has an intensity that corresponds to the pixel data. However, as previously described, the intensity of the light emitted from the semiconductor laser can vary depending on the temperature of the semiconductor laser  52 . Therefore, the intensity of the light emitted from the light source device  50  could have an intensity which does not correspond to the pixel data. 
     A-2. COMPARATIVE EXAMPLE 
       FIG. 3  is a timing chart showing an operation of a light source device currently known in the art as a comparative example.  FIG. 3A  shows the pixel data provided to the light source device.  FIG. 3B  shows the drive current supplied to a semiconductor laser.  FIG. 3C  shows the temperature of the semiconductor laser.  FIG. 3D  shows the threshold current of the semiconductor laser.  FIG. 3E  shows the intensity of the light emitted from the semiconductor laser. 
     As shown in  FIG. 3A , the pixel data stays in zero during the period T 1 , has a relatively large value during the period T 2 , and has a relatively small value during the period T 3 . As shown  FIG. 3B , the drive current of the semiconductor laser is set to the value corresponding to the pixel data. More specifically, the drive current of the semiconductor laser is set to zero during the period T 1 , has a large value during the period T 2 , and has a relatively small value during the period T 3 . 
     As the drive current varies, the temperature of the semiconductor laser varies as, for example, shown  FIG. 3C . Specifically, the temperature of the semiconductor laser increases gradually during the period T 2  after the drive current has been set to a constant value, and then gradually drops during the period T 3  after the drive current has been reduced. Further, as the temperature of the semiconductor laser varies, the threshold current of the semiconductor laser varies, as shown in  FIG. 3D . Specifically, the threshold current of the semiconductor laser decreases as the temperature rises in the period T 2 , while increases as the temperature drops during the period T 3 . As a result, as shown  FIG. 3E , the emission amount of the semiconductor laser increases rapidly and then gently increases during the period T 2 , and decreases rapidly and then gently decreases during the period T 3 . 
     The profile of the emission amount shown  FIG. 3E  is preferably equivalent or similar to the profile of the pixel data shown in  FIG. 3A . However, as may be observed from the comparison between  FIG. 3A  and  FIG. 3E , the two profiles are significantly different from each other. This is because the threshold current is significantly varied due to the change in temperature of the semiconductor laser as shown in  FIG. 3D . 
     If the light source device currently known in the art, even in the case in which a solid image or image with even luminance is supposed to be displayed on the screen, an image with a distributed luminance may be generated. More specifically, it is assumed that each of the line images of the solid image is drawn from a first side to a second side. When the first side of each of the line images is drawn, the emission amount is relatively small because the temperature of the semiconductor laser is relatively low, and the threshold current is relatively high. In contrast, when the second side of each of the line images is drawn, the emission amount is relatively large because the temperature of the semiconductor laser is relatively high, and the threshold current is relatively low. As a result, the luminance of the first side of the solid image displayed on the screen is lower than the luminance in the second side. 
     Therefore, in the present embodiment, the configuration of the light source device  50  is devised so that the profile of the emission amount is equivalent or the same as the profile of the pixel data. 
     It should be noted that the problem shown in  FIG. 3  becomes even more prominent in, for example, a semiconductor laser where a thermal lens effect is used. Specifically, when the temperature of the semiconductor laser is increased in accordance with the drive current, the threshold current decreases, thus the emission amount of the semiconductor laser increases. By contrast, when the temperature of the semiconductor laser is low in accordance with the drive current, the threshold current becomes large, thus the emission amount of the semiconductor laser decreases. Here, the thermal lens effect denotes the phenomenon that occurs when irradiation with the laser beam causes the local elevation of temperature, which in turn generates the refractive index distribution. 
     A-3. CONFIGURATION OF LIGHT SOURCE DEVICE 
       FIG. 4  is an explanatory diagram showing a schematic configuration of the light source device  50  of  FIG. 1 . As shown  FIG. 4 , the light source device  50  is provided with a semiconductor laser (LD)  52  and a control circuit  54  for controlling the operation of the semiconductor laser  52 . The semiconductor laser  52  uses the thermal lens effect. The control circuit  54  is provided with a current driver  110 , a light-sensitive element (PD)  130 , a current-to-voltage (I/V) converter  140 , a threshold current estimator  150 , and a differential efficiency adjustment section  300 . 
     The current driver  110  supplies the semiconductor laser  52  with a drive current I corresponding to a threshold current command value Dapc 1 , a grayscale current command value Dapc 2 , and the pixel data D. These three signals Dapc 1 , Dapc 2 , and D will be described more fully below. 
     The semiconductor laser  52  emits the laser beam in accordance with the drive current I supplied from the current driver  110 . 
     The light-sensitive element  130  outputs the current corresponding to the intensity of the light emitted from the semiconductor laser  52 . 
     The I/V converter  140  outputs the voltage corresponding to the current received from the light-sensitive element  130 . The voltage output from the IV converter  140  depends on the intensity of the light emitted from the semiconductor laser  52 . Therefore, the voltage output from the I/V converter  140  is also hereinafter simply referred to as “the emission amount L.” 
     The threshold current estimator  150  estimates the threshold current I th  of the semiconductor laser  52  using the voltage or emission amount L output from the I/V converter  140  and the drive current I supplied from the current driver  110  to the semiconductor laser  52 . The estimated threshold current I th  is fed-back to the current driver  110  in real time as the threshold current command value Dapc 1 . 
     It should be noted that the control circuit  54  in the present embodiment comprises a control section. Further, the current driver  110  comprises a current supply section and the threshold current estimator  150  comprises an estimation section. 
     The differential efficiency adjustment section  300  adjusts the grayscale current command value Dapc 2  using the emission amount L and the pixel data D, and transmits it to the current driver  110 . Further, the differential efficiency adjustment section  300  adjusts a differential efficiency characteristic value of the semiconductor laser as more fully described below. The differential efficiency characteristic value is used when the threshold current estimator  150  estimates the threshold current I th  using the adjusted grayscale current command value Dapc 2 . 
       FIGS. 5A through 5C  are explanatory diagrams for explaining the function of the differential efficiency adjustment section  300 .  FIG. 5A  shows a graph representing a relationship between the pixel data D and the emission amount of the laser. Here, the target light amount T that the semiconductor laser  52  should emit in accordance with the pixel data D is represented as T=m·D which is shown as line G 1  in the graph of  FIG. 5A . In comparison, the actual measured emission amount Y measured by the light-sensitive element  130  and the I/V converter  140  is represented by the line Y=a·D+b. It should be noted that m is a coefficient, and a and b are variables. Further, the actual measured emission amount Y corresponds to the emission amount L which is emitted using the configuration shown in  FIG. 1 . 
     As previously described, semiconductor lasers typically have emission amounts which increases linearly in accordance with the current value supplied to the semiconductor lasers when the current supplied to the semiconductor lasers exceeds a threshold current. In the present specification, this characteristic is referred to as the “differential efficiency η.” It should be noted that it is known that the differential efficiency η varies in accordance with, for example, the temperature of the semiconductor laser. 
     As shown in  FIG. 5A , the target light amount corresponding to certain pixel data D k  is T k , and the actual measured emission amount is Y k . The difference between Y k  and T k  can be represented as a light amount error δ k .  FIG. 5B  shows the case where the characteristics of the laser vary so as to make the variable a of the actual measured emission amount Y larger, and  FIG. 5C  shows where the characteristics of the laser vary so as to make the variable a of the actual measured emission amount Y smaller. Since the variable a is a variable which affects to the differential efficiency η, it can be understood that it is desirable to correct the differential efficiency η in the both cases shown in  FIGS. 5B and 5C . The differential efficiency adjustment section  300  sets the grayscale current command value Dapc 2  so that the light amount error δ k  is minimized, thereby correcting the differential efficiency η. It should be noted that the variable b is a variable corresponding to the threshold current I th , and the threshold current I th  is corrected by the threshold current estimator  150 . 
       FIG. 6  is an explanatory diagram showing an internal configuration of the current driver  110  of  FIG. 4 . It should be noted that  FIG. 6  also shows the semiconductor laser  52 . The current driver  110  is provided with a drive current determination section  110   a,  a threshold current determination section  110   b,  and a light emission current determination section  110   c.    
     As is well known in the art, the semiconductor laser  52  emits light when the drive current I exceeds the threshold current I th . In other words, the emission amount L of the semiconductor laser  52  depends on the difference between the drive current I and the threshold current I th . Therefore, in the present embodiment, the difference between the drive current I and the threshold current I th  is referred to as “a light emission current” I d . 
     The drive current determination section  110   a  is provided with a current mirror circuit including two p-MOS transistors Tm 1  and Tm 2 . The drain terminal of the first transistor Tm 1  is connected to the semiconductor laser  52  and the drain terminal of the second transistor Tm 2  is connected to the threshold current determination section  110   b  and the light emission current determination section  110   c.    
     The threshold current determination section  110   b  is provided with a constant current source S 1 . The constant current source S 1  is supplied with the threshold current command value Dapc 1 , and the constant current source S 1  provides the current SI th  corresponding to the threshold current command value Dapc 1 . It should be noted that the current SI th  corresponds to the threshold current I th . 
     The light emission current determination section  110   c  is provided with a constant current source S 2  and an n-MOS transistor T i  connected in series with each other. The constant current source S 2  is supplied with the grayscale current command value Dapc 2 , and the constant current source S 2  provides the current SI g  corresponding to the grayscale current command value Dapc 2 . It should be noted that in the present embodiment, since the grayscale current command value Dapc 2  is a constant value, the current SI g  is constant. 
     Further, the light emission current determination section  110   c  is provided with four sets of switches Sw 1 -Sw 4  and n-MOS transistors Td 1 -Td 4  connected in parallel to each other. It should be noted that the switch (e.g., Sw 1 ) and the transistor (e.g., Td 1 ) of each of the sets are connected in series with each other. The four sets of switches Sw 1 -Sw 4  and transistors Td 1 -Td 4  are disposed in parallel to the threshold current determination section  110   b.  Further, the gate terminals of the four transistors Td 1 -Td 4  are all connected to the gate terminal of the transistor T i . 
     The four switches Sw 1 -Sw 4  are provided with the pixel data D composed of four bits. It should be noted that although the pixel data D is composed of four bits in  FIG. 6 , it is also possible to form the pixel data D with a fewer or larger number of bits. In such cases, it is sufficient to provide a number of sets of switches and transistors that corresponds to the number of bits of the pixel data D. 
     When each of the switches Sw 1 -Sw 4  is set to the ON state in accordance with the pixel data D, the current flows through the corresponding transistor Td 1 -Td 4 . When the first switch Sw 1  is set to be the ON state in accordance with the first bit or most significant bit of pixel data D, the current of ½·SI g  flows through the first transistor Td 1 . Similarly, when the second switch Sw 2  is set to be the ON state in accordance with the second bit of the pixel data D, the current of ¼·SI g  flows through the second transistor Td 2 . When the third switch Sw 3  is set to be the ON state in accordance with the third bit of the pixel data D, the current of ⅛·SI g  flows through the third transistor Td 3 . When the fourth switch Sw 4  is set to be the ON state in accordance with the fourth bit or least significant bit of the pixel data D, the current of 1/16·SI g  flows through the fourth transistor Td 4 . 
     The current SId, which is the sum of the currents flowing through the four transistors Td 1 -Td 4 , is at the maximum ( 15/16·SI g ) when all of the switches Sw 1 -Sw 4  are set to be the ON state. It should be noted that the current SId corresponds to the light emission current Id. 
     The current SI, which is the sum of the current SI th  supplied to the threshold current determination section  110   b  and the current SI d  supplied to the light emission current determination section  110   c,  flows through the second transistor Tm 2  of the drive current determination section  110   a.  In the present embodiment, since the two transistors Tm 1  and Tm 2  have the same size (channel length L/channel width W), a drive current I having the same value as the current SI flows through the first transistor Tm 1 . Further, the drive current I is supplied to the semiconductor laser  52 . It should be noted that the sizes (L/W) of the two transistors Tm 1  and Tm 2  can also be different from each other. 
     As described above, the drive current I is determined using the current SI th  corresponding to the threshold current I th  and the current SI d  corresponding to the light emission current Id. The current SI th  corresponding to the threshold current I th  is determined in accordance with the threshold current command value Dapc 1 . The current SI d  corresponding to the light emission current Id is determined in accordance with the two signals Dapc 2  and D. 
     By adopting the configuration shown in  FIG. 6 , the current driver  110  is capable of efficiently supplying the semiconductor laser  52  with the drive current I including the threshold current I th  and the light emission current I d  exceeding the threshold current I th . 
     It should be noted that the threshold current determination section  110   b  comprises a first circuit and the light emission current determination section  110   c  comprises the second circuit in the claims recited below. 
     As explained with reference to  FIGS. 4 and 6 , the threshold current estimator  150  estimates the threshold current I th  using the drive current I and the emission amount L, and feeds-back the estimated threshold current I th  to the current driver  110  in real time. Further, the differential efficiency adjustment section  300  adjusts the grayscale current command value Dapc 2  using the emission amount L and the pixel data D, and feeds it back to the threshold current estimator  150  and the current driver  110 . Further, the current driver  110  determines the drive current I based on the pixel data D, the estimated threshold current I th , and the adjusted grayscale current command value Dapc 2 . According to the present configuration, the semiconductor laser  52  can emit the laser beam with the emission amount L corresponding to the light emission current I d . 
     It should be noted that it is sufficient for the operation band of the threshold current estimator  150  and the differential efficiency adjustment section  300  to correspond to a response speed which is higher than the temperature response of the semiconductor laser  52 . For example, in the case in which the temperature response speed of the semiconductor laser  52  is several tens of microseconds, the operation band of the threshold current estimator  150  and the differential efficiency adjustment section  300  of several microseconds of several hundreds kHz is sufficient. 
     A-4. OPERATION OF LIGHT SOURCE DEVICE 
       FIG. 7  is a timing chart showing an operation of the light source device  50  according to the present invention.  FIG. 7A  shows the pixel data D provided to the current driver  110 .  FIG. 7B  shows the light emission current I d  corresponding to the pixel data D determined by the light emission current determination section  110   c.    FIG. 7C  shows the threshold current I th  of the semiconductor laser  52  estimated by the threshold current estimator  150 .  FIG. 7D  shows the drive current I supplied from the current driver  110  to the semiconductor laser  52 . It should be noted that the threshold current I th  shown in  FIG. 7C  is also illustrated  FIG. 7D  as a dotted line.  FIG. 7E  shows the emission amount L of the semiconductor laser  52 . 
     When the pixel data D varies as shown in the part  FIG. 7A , the light emission current I d  varies in accordance with the pixel data D as shown in the  FIG. 7B . As previously described, the threshold current I th  of the semiconductor laser  52  can vary in accordance with the temperature of the semiconductor laser. The threshold current I th  varies as, for example, shown in  FIG. 7C . Since the drive current I is represented by the sum of the threshold current I th  (shown in  FIG. 7C ) and the light emission current I d  (shown in  FIG. 7B ), the semiconductor laser  52  is provided with the drive current I shown in  FIG. 7D . As a result, the semiconductor laser  52  emits the light with the emission amount L shown in  FIG. 7E . 
     As described above, since the drive current I, which is the sum of the threshold current I th  and the light emission current I d  corresponding to the pixel data D, is supplied to the semiconductor laser  52  in the present embodiment, it becomes possible to make the profile of the pixel data D (shown in  FIG. 7A ) and the profile of the emission amount L (shown in  FIG. 7E ) the same. 
     A-5. THRESHOLD CURRENT ESTIMATOR 
     In order to configure the threshold current estimator  150 , a method of operating a semiconductor laser  52  will now be described. 
     The rate equation of the semiconductor laser is represented by the following formulas (1), (2). 
     
       
         
           
             
               
                 
                   
                     
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     Here, the symbol I denotes the current or drive current injected into the light emitting or active region, e denotes a charge, and V denotes the volume of the light emitting region. The symbol N denotes the density of the carriers injected into the light emitting region, and N c  denotes the carrier density for starting amplification of the light. The symbol N c  denotes the relaxation time or the time constant of losing the carrier density of the carriers. The symbol P denotes the energy density or photon number density of the laser beam. The symbol τ p  denotes the relaxation time or time constant at which the photon number density is lost. The symbol A denotes a coefficient related to the stimulated emission. 
     Formula (1) shows that the temporal variation of the number of carriers is obtained by subtracting the number of carriers lost by the relaxation and the number of the carriers contributing to the effective stimulated emission from the number of the carriers corresponding to the injected current. Formula (2) shows that the temporal variation of the number of photons is obtained by subtracting the number of photons lost by the relaxation from the number of the photons generated by the effective stimulated emission. 
     The photon number density P in the steady state is represented as the following formula (3) using the formulas (1), (2). 
     
       
         
           
             
               
                 
                   
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     Next, the thermal lens effect of the semiconductor laser will be described. Assuming that the photon number density in the light emitting region increases due to the thermal lens effect, the rate equation is represented by the following formulas (4) and (5). It should be noted that formulas (4) and (5) are obtained by replacing the coefficient A related to the stimulated emission in formulas (2) and (3) with the coefficient A·F. Here, the coefficient F is a coefficient related to the effect of the thermal lens. 
     
       
         
           
             
               
                 
                   
                     
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     Further, the photon number density P in the steady state is represented by the following formula (6). It should be noted that formula (6) is obtained by replacing the coefficient A in formula (3) with the coefficient A·F. 
     
       
         
           
             
               
                 
                   
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                               · 
                               F 
                               · 
                               
                                 τ 
                                 p 
                               
                             
                           
                           + 
                           
                             N 
                             c 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     G 
                     = 
                     
                       
                         τ 
                         ρ 
                       
                       
                         e 
                         · 
                         V 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Since the coefficient F is a coefficient related to the effect of the thermal lens, when the thermal lens effect becomes large in association with increase in the drive current I, the value of the coefficient F becomes large and the threshold current I th  becomes small. By contrast, when the thermal lens effect becomes small in association with decrease in the drive current I, the value of the coefficient F becomes small, and the threshold current I th  becomes large. 
     Incidentally, taking the proportion of the light emitted from the light emitting region and the sensitivities of the light-sensitive element  130  and the I/V converter  140  into consideration, the emission amount L of the semiconductor laser is represented by the following formula (7) using the coefficient M. 
         L=M ( I−I   th )   (7) 
     The response of the temperature of the light emitting region corresponding to the drive current I is represented by the following formula (8) assuming that a calorific value Q is proportional to the drive current I. 
     
       
         
           
             
               
                 
                   
                     
                       
                         Q 
                         = 
                           
                          
                         
                           a 
                           · 
                           I 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             C 
                              
                             
                               
                                  
                                 0 
                               
                               
                                  
                                 t 
                               
                             
                           
                           + 
                           
                             k 
                             · 
                             θ 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     Here, the symbol a denotes a coefficient. Further, the symbol  0  denotes the temperature of the light emitting region, C denotes the calorific capacity of the light emitting region, and k denotes a heat conduction coefficient. 
     Assuming that τ C/k is satisfied, the following formula (9) is obtained from formula (8). 
     
       
         
           
             
               
                 
                   
                     
                       τ 
                        
                       
                         
                            
                           θ 
                         
                         
                            
                           t 
                         
                       
                     
                     + 
                     θ 
                   
                   = 
                   
                     
                       a 
                       k 
                     
                      
                     I 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The threshold current I th  depends on the thermal lens effect (the coefficient F of formula (6)), and the thermal lens effect depends on the temperature of the light emitting region. Therefore, the threshold current I th  depends on the temperature of the light emitting region. Assuming that the threshold current I th  is a direct function of the temperature θ of the light emitting region, the following formula (10) is obtained. Note that p and q are constants. 
       θ=− p·I   th   +q    (10) 
     By substituting formula (10) for θ in formula (9), formula (11) is obtained. Note that α and β are constants. 
     
       
         
           
             
               
                 
                   
                     
                       
                          
                         
                           I 
                           th 
                         
                       
                       
                          
                         t 
                       
                     
                     = 
                     
                       
                         
                           - 
                           
                             I 
                             th 
                           
                         
                         + 
                         α 
                         - 
                         
                           β 
                            
                           
                               
                           
                            
                           I 
                         
                       
                       τ 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     α 
                     = 
                     
                       q 
                       p 
                     
                   
                    
                   
                     
 
                   
                    
                   β 
                   = 
                   
                     a 
                     
                       p 
                       · 
                       k 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     The constants α and β are obtained by measuring the current-emission amount. Specifically, in the case in which the semiconductor laser  52  is provided with a direct current to emit light, the right side of formula (11) is equal to zero. Therefore, I th =α−β·I is satisfied. Therefore, when the semiconductor laser  52  is made to emit light with the direct current, formula (12) is satisfied. Further, when the semiconductor laser  52  is made to emit light with an alternating current, more specifically, in the case in which the semiconductor laser is made to emit light with a shorter cycle time than the temperature response of the semiconductor laser  52 , such as in a blink of light, formula (13) is satisfied. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           L 
                           
                             d 
                              
                             
                                 
                             
                              
                             c 
                           
                         
                         = 
                           
                          
                         
                           M 
                            
                           
                             { 
                             
                               I 
                               - 
                               
                                 ( 
                                 
                                   α 
                                   - 
                                   
                                     β 
                                      
                                     
                                         
                                     
                                      
                                     I 
                                   
                                 
                                 ) 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           M 
                            
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     + 
                                     β 
                                   
                                   ) 
                                 
                                  
                                 I 
                               
                               - 
                               α 
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             M 
                              
                             
                               ( 
                               
                                 1 
                                 + 
                                 β 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               I 
                               - 
                               
                                 α 
                                 
                                   1 
                                   + 
                                   β 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     L 
                     
                       a 
                        
                       
                           
                       
                        
                       c 
                     
                   
                   = 
                   
                     M 
                      
                     
                       ( 
                       
                         I 
                         - 
                         
                           I 
                           th 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     By measuring of the current-emission amount with the direct current and the alternating current, the constants α, β can be obtained using formulas (12) and (13). 
     In the present embodiment, the threshold current estimator  150  is configured using an observer in modern control theory. From the result of the study using numerical calculation, it has been known that the accuracy of the parameter a described above has a significant influence on the estimation accuracy of the threshold current I th . Therefore, in the present embodiment, the observer is configured as described below. 
     The threshold current I th  and the parameter α are selected as state variables. Further, the scaled state variables are hereinafter used so that the estimated values of the threshold current I th  can be fed-back directly to the current driver  110 . 
     The output current I or drive current of the current driver  110  can be represented by formula (14) using the constants H 1  and H 2  (see  FIG. 6 ). It is assumed that the scaled current values are u=I/H 1 , x=I th /H 1 . In this case, formula (15) can be obtained from formula (14). 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     
                       H 
                        
                       
                           
                       
                        
                       
                         1 
                         · 
                         Dapc 
                       
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       H 
                        
                       
                           
                       
                        
                       
                         2 
                         · 
                         Dapc 
                       
                        
                       
                           
                       
                        
                       
                         2 
                         · 
                         D 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   u 
                   = 
                   
                     
                       Dapc 
                        
                       
                           
                       
                        
                       1 
                     
                     + 
                     
                       
                         
                           
                             H 
                              
                             
                                 
                             
                              
                             2 
                           
                           
                             H 
                              
                             
                                 
                             
                              
                             1 
                           
                         
                         · 
                         Dapc 
                       
                        
                       
                           
                       
                        
                       
                         2 
                         · 
                         D 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Further, formula (16) is obtained from formula (7), and formula (17) is obtained from formula (11). Note that M 1 =M·H 1 , and α 1 =α/H 1 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             L 
                             = 
                               
                              
                             
                               
                                 M 
                                 · 
                                 H 
                               
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                 ( 
                                 
                                   
                                     I 
                                     
                                       H 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                   - 
                                   
                                     
                                       I 
                                       th 
                                     
                                     
                                       H 
                                        
                                       
                                           
                                       
                                        
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                               
                              
                             
                               M 
                                
                               
                                   
                               
                                
                               1 
                                
                               
                                 ( 
                                 
                                   u 
                                   - 
                                   x 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                      
                     
                       
 
                     
                     ∴ 
                     y 
                   
                   = 
                   
                     L 
                     = 
                     
                       M 
                        
                       
                           
                       
                        
                       1 
                        
                       
                         ( 
                         
                           u 
                           - 
                           x 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 
                   
                     
                       1 
                       
                         H 
                          
                         
                             
                         
                          
                         1 
                       
                     
                      
                     
                       
                          
                         
                           I 
                           th 
                         
                       
                       
                          
                         t 
                       
                     
                   
                   = 
                   
                     
                       
                         
                           
                             - 
                             
                               
                                 I 
                                 th 
                               
                               
                                 H 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                           + 
                           
                             α 
                             
                               H 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                           - 
                           
                             β 
                              
                             
                               I 
                               
                                 H 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                           
                         
                         τ 
                       
                        
                       
                         
 
                       
                       ∴ 
                       
                         
                            
                           x 
                         
                         
                            
                           t 
                         
                       
                     
                     = 
                     
                       
                         
                           - 
                           x 
                         
                         + 
                         
                           α 
                            
                           
                               
                           
                            
                           1 
                         
                         - 
                         
                           β 
                            
                           
                               
                           
                            
                           u 
                         
                       
                       τ 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Assuming that the state variables are [x, α 1 ] T , the state equation of the plant can be represented by formula (18) using the formulas (16) and (17). It should be noted that the plant includes the semiconductor laser  52 , the light-sensitive element  130 , and the I/V converter  140 , as shown in  FIG. 4 . 
     
       
         
           
             
               
                 
                   
                     
                       w 
                       . 
                     
                     = 
                     
                       
                         A 
                          
                         
                             
                         
                          
                         w 
                       
                       + 
                       
                         B 
                          
                         
                             
                         
                          
                         u 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     y 
                     = 
                     
                       
                         C 
                          
                         
                             
                         
                          
                         w 
                       
                       + 
                       
                         D 
                          
                         
                             
                         
                          
                         u 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     w 
                     = 
                     
                       [ 
                       
                         
                           
                             x 
                           
                         
                         
                           
                             
                               α 
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       A 
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 - 
                                 
                                   1 
                                   τ 
                                 
                               
                             
                             
                               
                                 1 
                                 τ 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       B 
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 - 
                                 
                                   β 
                                   τ 
                                 
                               
                             
                           
                           
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       C 
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   - 
                                   M 
                                 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       D 
                       = 
                       
                         M 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     By configuring the observer, namely the threshold current estimator  150 , using the state equation of formula (18), the threshold current I th  can be corrected. More specifically, the threshold current estimator  150  can be represented by formula (19). 
     
       
         
           
             
               
                 
                   
                     
                       w 
                       
                         ^ 
                         . 
                       
                     
                     = 
                     
                       
                         A 
                          
                         
                             
                         
                          
                         
                           w 
                           ^ 
                         
                       
                       + 
                       
                         B 
                          
                         
                             
                         
                          
                         u 
                       
                       - 
                       
                         F 
                          
                         
                           ( 
                           
                             y 
                             - 
                             
                               y 
                               ^ 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       y 
                       ^ 
                     
                     = 
                     
                       
                         C 
                          
                         
                             
                         
                          
                         
                           w 
                           ^ 
                         
                       
                       + 
                       
                         D 
                          
                         
                             
                         
                          
                         u 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       w 
                       ^ 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               x 
                               ^ 
                             
                           
                         
                         
                           
                             
                               
                                 α 
                                 ^ 
                               
                                
                               
                                   
                               
                                
                               1 
                             
                           
                         
                       
                       ] 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       A 
                       = 
                       
                         [ 
                         
                           
                             
                               
                                 - 
                                 
                                   1 
                                   τ 
                                 
                               
                             
                             
                               
                                 1 
                                 τ 
                               
                             
                           
                           
                             
                               0 
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                     
                     , 
                     
                       B 
                       = 
                       
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     - 
                                     
                                       β 
                                       τ 
                                     
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                               
                             
                             ] 
                           
                            
                           
                             
 
                           
                            
                           C 
                         
                         = 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     - 
                                     M 
                                   
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                       
                     
                     , 
                     
                       D 
                       = 
                       
                         M 
                          
                         
                             
                         
                          
                         1 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     F 
                     = 
                     
                       [ 
                       
                         
                           
                             
                               f 
                               τ 
                             
                           
                         
                         
                           
                             
                               
                                 f 
                                 0 
                               
                               τ 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Note that “̂” in the formula denotes an estimated value. The elements f/τ, f 0 /τ are feed-back coefficients. 
       FIG. 8  is an explanatory diagram showing a specific configuration of the light source device  50 . It should be noted that although  FIG. 8  is obtained by redrawing  FIG. 4  using formulas (15) and (19), the differential efficiency adjustment section  300  is omitted from the drawing for the sake of convenience. Specifically, the current driver  110  is represented by formula (15) and the threshold current estimator  150  is represented by formula (19). 
     The current driver  110  includes a multiplier  111 , two amplifiers  112  and  113 , and an adder  114 . The multiplier  111  multiplies the threshold current command value Dapc 2  by the pixel data D to output the signal Dapc 2 ·D. The first amplifier  112  amplifies the signal Dapc 2 ·D to be H 2 /H 1  times as large to output the signal H 2 /H 1 ·Dapc 2 ·D. It should be noted that the grayscale current command value Dapc 2  is adjusted by the differential efficiency adjustment section  300  described more fully below. 
     The second amplifier  113  amplifies the signal Dapc 1  to be the same value. The adder  114  adds the two signals H 2 /H 1 ·Dapc 2 ·D and Dapc 1  output respectively from the two amplifiers  112  and  113  together. As a result, the signal u represented by formula (15) is output form the adder  114 . 
     It should be noted that the second amplifier  113 , which is provided in the present embodiment can be eliminated. 
     The threshold current estimator  150  includes five amplifiers  151 - 155 , three computing units  156 - 158 , an integrator  159 , and an extractor  150   a    
     The integrator  159  integrates the signal d(ŵ)/dt to output the signal ŵ. 
     The first amplifier  151  amplifies the signal ŵ A times to output the signal A·ŵ. The second amplifier  152  amplifies the signal u B times to output the signal B·u. The third amplifier  153  amplifies the signal ŵ C times to output the signal C·ŵ. The fourth amplifier  154  amplifies the signal u D times to output the signal D·u. The fifth amplifier  155  amplifies the signal (y−ŷ) F times to output the signal F·(y−ŷ). 
     The first computing unit  156  adds the signals A·ŵ and B·u to each other, and subtracts the signal F·(y−ŷ) therefrom, thereby outputting the signal d(ŵ)/dt represented by formula (19). The second computing unit  157  adds the signals C·ŵ and D·u to each other to output the signal ŷ represented by formula (19). The third computing unit  158  subtracts the signal ŷ from the signal y to output the signal (y−ŷ). It should be noted that the signal y represents the measured value of the emission amount L, and the signal ŷ represents the estimated value of the emission amount L of formula (16). 
     The extractor  150   a  extracts the signal {circumflex over (x)} from the signal ŵ, and feeds-back the signal {circumflex over (x)} to the current driver  110  as the threshold current command value Dapc 1 . 
     By substituting the contents of the coefficients A-D and F for the coefficients A-D and F in the equations of formula (19), formula (20) can be obtained. Further, by developing formula (20), formula (21) can be obtained. 
     
       
         
           
             
               
                 
                   
                     w 
                     
                       ^ 
                       . 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               x 
                               
                                 ^ 
                                 . 
                               
                             
                           
                         
                         
                           
                             
                               
                                 α 
                                 
                                   ^ 
                                   . 
                                 
                               
                                
                               1 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   - 
                                   
                                     1 
                                     τ 
                                   
                                 
                               
                               
                                 
                                   1 
                                   τ 
                                 
                               
                             
                             
                               
                                 0 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     α 
                                     ^ 
                                   
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   - 
                                   
                                     β 
                                     τ 
                                   
                                 
                               
                             
                             
                               
                                 0 
                               
                             
                           
                           ] 
                         
                          
                         u 
                       
                       - 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   f 
                                   τ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     f 
                                     0 
                                   
                                   τ 
                                 
                               
                             
                           
                           ] 
                         
                          
                         
                           ( 
                           
                             y 
                             - 
                             
                               y 
                               ^ 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       y 
                       ^ 
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     - 
                                     M 
                                   
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                          
                         
                           [ 
                           
                             
                               
                                 
                                   x 
                                   ^ 
                                 
                               
                             
                             
                               
                                 
                                   
                                     α 
                                     ^ 
                                   
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                           
                           ] 
                         
                       
                       + 
                       
                         M 
                          
                         
                             
                         
                          
                         
                           1 
                           · 
                           u 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       x 
                       
                         ^ 
                         . 
                       
                     
                     = 
                     
                       
                         
                           1 
                           τ 
                         
                          
                         
                           ( 
                           
                             
                               
                                 α 
                                 ^ 
                               
                                
                               1 
                             
                             - 
                             
                               x 
                               ^ 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         
                           β 
                           τ 
                         
                          
                         u 
                       
                       - 
                       
                         
                           f 
                           τ 
                         
                          
                         
                           ( 
                           
                             y 
                             - 
                             
                               y 
                               ^ 
                             
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       
                         α 
                         
                           ^ 
                           . 
                         
                       
                        
                       1 
                     
                     = 
                     
                       
                         - 
                         
                           
                             f 
                             0 
                           
                           τ 
                         
                       
                        
                       
                         ( 
                         
                           y 
                           - 
                           
                             y 
                             ^ 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       y 
                       ^ 
                     
                     = 
                     
                       M 
                        
                       
                           
                       
                        
                       1 
                        
                       
                         ( 
                         
                           u 
                           - 
                           
                             x 
                             ^ 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
       FIG. 9  is an explanatory diagram showing a circuit diagram of the light source device  50 . It should be noted that although  FIG. 9  is obtained by redrawing  FIG. 4  using formula (21), the differential efficiency adjustment section  300  is omitted from the drawing for the sake of convenience. 
     As shown in the drawing, the light source device  50  is provided with a drive current measurement section  160  for measuring the drive current I (the signal u) supplied to the semiconductor laser  52 . The drive current measurement section  160  is provided with a differential amplifier  161  and an amplifier  162 . The two terminals of the differential amplifier  161  are connected to both ends of a resistor Rs connected to the anode of the semiconductor laser  52 . The differential amplifier  161  receives the voltages of the both ends of the resistor Rs and outputs the difference in voltage between the both ends. It should be noted that the difference in voltage is represented by I·Rs. The amplifier  162  multiplies the difference in voltage 1/(Rs·H 1 ) times. As a result, the multiplier  162  outputs the signal I/H 1 , namely the signal u. 
     The threshold current estimator  150  includes five differential amplifiers  201 - 205 , five amplifiers  211 - 215 , and two integrators  221  and  222 . 
     The first integrator  221  integrates the signal d({circumflex over (x)})/dt to output the signal {circumflex over (x)}. The second integrator  222  integrates the signal d({circumflex over (α)} 1 )/dt to output the signal {circumflex over (α)} 1 . 
     The first differential amplifier  201  subtracts the signal {circumflex over (x)} from the signal {circumflex over (α)} 1  to output the signal ({circumflex over (α)} 1 −{circumflex over (x)}). The first amplifier  211  amplifies the signal ({circumflex over (α)} 1 −{circumflex over (x)})1/τ times to output the signal 1/τ·({circumflex over (α)} 1 −{circumflex over (x)}). The second amplifier  212  amplifies the signal u β/τ times to output the signal β/τ·u. The second differential amplifier  202  subtracts the signal β/τ·u from the signal 1/τ·({circumflex over (α)} 1 −{circumflex over (x)}) to output the signal [1/τ·({circumflex over (α)} 1 −{circumflex over (x)})−β/τ·u]. The third amplifier  213  amplifies the signal (y−ŷ)f/τ times to output the signal f/τ·(y−ŷ). The third differential amplifier  203  subtracts the signal f/τ·(y−ŷ) from the signal [1/τ·({circumflex over (α)} 1 −−{circumflex over (x)})−β/τ·u] to output the signal d({circumflex over (x)})/dt represented by formula (21). 
     The fourth amplifier  214  amplifies the signal (y−ŷ)−f 0 /τ times to output the signal d({circumflex over (α)} 1 )/dt represented by formula (21). 
     The fourth differential amplifier  204  subtracts the signal {circumflex over (x)} from the signal u to output the signal (u−{circumflex over (x)}). The fifth amplifier  215  amplifies the signal (u−{circumflex over (x)}) M 1  times to output the signal ŷ represented by the formula (21). The value M 1  represents the differential efficiency η of the semiconductor laser  52 , and is hereinafter also referred to as “the differential efficiency characteristic value M 1 .” Specifically, the signal ŷ represents the estimated value of the emission amount of the semiconductor laser  52  obtained by the estimated value {circumflex over (x)}. It should be noted that the fifth amplifier  215  is formed of a variable gain amplifier the gain of which can arbitrarily be controlled, and the gain M 1  is set in accordance with the grayscale current command value Dapc 2  adjusted by the differential efficiency adjustment section  300  as described more fully below. 
     The fifth differential amplifier  205  subtracts the signal ŷ from the signal y to output the signal (y−ŷ). 
     As previously above, since the threshold current estimator  150  uses the two state variables x and α 1 , the threshold current estimator  150  is provided with the first integrator  221  for integrating the signal d({circumflex over (x)})/dt, which is the derivative of the signal {circumflex over (x)}, in order to obtain the signal {circumflex over (x)}, and the second integrator  222  for integrating the signal d({circumflex over (α)} 1 )/dt, which is the derivative of the signal {circumflex over (α)} 1 , to obtain the signal {circumflex over (α)} 1 . The threshold current estimator  150  obtains the signal ŷ using the signal u and the signal {circumflex over (x)} output from the first integrator  221 . Further, the threshold current estimator  150  obtains the signal d({circumflex over (α)} 1 )/dt to be provided to the second integrator  222  using the signal (y−ŷ). Further, the threshold current estimator  150  obtains the signal d({circumflex over (x)})/dt to be provided to the first integrator  221  using the signal u, the signal (y−ŷ), the signal {circumflex over (x)} output from the first integrator  221 , and the signal {circumflex over (α)} 1  output from the second integrator  222 . 
     As described above, by using the two state variables x, α 1 , the estimated value {circumflex over (x)} of the threshold current can accurately be obtained. Further, since the threshold current estimator  150  uses the differential efficiency characteristic value M 1  corresponding to the grayscale current command value Dapc 2  adjusted by the differential efficiency adjustment section  300 , the variation in the characteristics of the semiconductor light emitting element is reflected in the estimated value, meaning that the estimation accuracy thereof can be improved. 
     The light source device  50  further includes a comparator  171  and a switch  172 . The comparator  171  compares the signal y (the emission amount L) with zero If the signal y is equal to or greater than zero, the comparator  171  sets the switch  172  to be the ON state. On this occasion, the switch  172  transmits the output of the differential amplifier  205 , namely the signal (y−ŷ). On the other hand, if the signal y is a negative value, the comparator  171  sets the switch  172  to be the OFF state. On this occasion, the switch  172  does not transmit the signal (y−ŷ) of the differential amplifier  205 , and instead outputs the value of zero. 
     Since the signal (y−ŷ) is not accurate in the non-emission period of the semiconductor laser  52 , it is not preferable to feed-back the signal (y−ŷ) to the two integrators  221  and  222  of the threshold current estimator  150 . Therefore, in the non-emission period, the feed-back loop is cut using the comparator  171  and the switch  172 . As a result, in the non-emission direction, the threshold current estimator  150  is only provided with the measurement value (u) of the drive current I. Further, the threshold current estimator  150  obtains the estimated value {circumflex over (x)} of the threshold current I th  in an open-loop manner. 
     As described above, since the feeding-back of the signal (y−ŷ) to the input of the threshold current estimator  150  is blocked in the non-emission period, the threshold current estimator  150  can obtain the estimated value {circumflex over (x)} of the threshold current in an open-loop manner. 
     Incidentally, when the non-emission period is long, an error in the estimated value ({circumflex over (x)}) of the threshold current, more specifically, the difference between the actual value (x) and the estimated value ({circumflex over (x)}) may gradually increase. However, when the semiconductor laser  52  starts emitting light again, the threshold current estimator  150  can output the correct estimated value ({circumflex over (x)}). It should be noted that a certain period of time (the recovery time) is required before the threshold current estimator  150  is able to output the correct estimated value ({circumflex over (x)}). Taking the recovery time into consideration, in the present embodiment, as shown in  FIG. 2 , an extra period T 0  is provided immediately before an effective period Tb. It should be noted that the extra period T 0  has a length equal to or greater than the recovery time. In the present embodiment, the control circuit  54  preliminarily supplies the current driver  110  with the drive current I in the extra period T 0 , thereby making the semiconductor laser  52  preliminarily emit light. Thus, the threshold current estimator  150  can output the correct estimated value ({circumflex over (x)}) in the entire period including the starting period of the effective period Tb. It should be noted that it is sufficient to mask the light emitted from the semiconductor laser  52  in the extra period T 0  so that light is not emitted to the screen  70 . 
     As described above, by making the semiconductor laser  52  preliminarily emit light immediately before making the semiconductor laser  52  start significant emission, it becomes possible to correctly obtain the estimated value {circumflex over (x)} of the threshold current immediately after the semiconductor laser  52  starts the significant emission. 
     As explained hereinabove, in the present embodiment, since the estimated value {circumflex over (x)} of the threshold current is obtained, and the drive current u is determined using the pixel data D and the estimated value {circumflex over (x)} of the threshold current is supplied to the semiconductor laser  52 , it is possible to make the semiconductor laser  52  accurately emit light with an intensity that accurately corresponds to the pixel data D even when the actual threshold current varies due to temperature variation. 
     Incidentally, the threshold current estimator  150  described herein can also be configured as a digital circuit. Here, by converting formula (19) into the discrete-time system with the sampling interval Ts using the trapezoidal approximation, formula (22) corresponding to formula (20) can be obtained. Further, when developing formula (22), formula (23) corresponding to formula (21) can be obtained. 
     
       
         
           
             
               
                 
                   
                     
                       
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     It should be noted that dŵ/dt corresponds to Ŵ k+1 , and the ŵ corresponds to Ŵ k . Further, y and ŷ correspond respectively to Y k  and Ŷ k , {circumflex over (x)} and {circumflex over (α)} 1  correspond respectively to {circumflex over (X)} k  and {circumflex over (X)}O k . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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       FIG. 10  corresponds to a drawing obtained by redrawing  FIG. 4  using formula (23).  FIG. 10  is roughly the same as  FIG. 9  except the point that the threshold current estimator  150  is formed of a digital circuit, and a drive current calculation section  180  is provided instead of the drive current measurement section  160 . It should be noted that other differences and relationship between  FIGS. 9 and 10  will be explained as necessary. 
     The drive current calculation section  180  is provided with a multiplier  181 , an amplifier  182 , and an adder  183 . The multiplier  181  multiplies the pixel data D by the grayscale current command value Dapc 2  to output the signal Dapc 2 ·D. The amplifier  182  amplifies the signal Dapc 2 ·D to be H 2 /H 1  times as large to output the signal H 2 /H 1 ·Dapc 2 ·D. The adder  183  adds the signal H 2 /H 1 ·Dapc 2 ·D and the signal Dapc 1  together to output the signal (Dapc 1 +H 2 /H 1 ·Dapc 2 ·D), namely the signal U k  (as described in formula (15)). It should be noted that the signal U k  corresponds to the signal u shown in  FIG. 9 . 
     As is understood from the explanations described above, the threshold current estimator  150  shown in  FIG. 9  estimates the threshold current I th  using the measured value (u) of the drive current I obtained by the drive current measurement section  160 . In contrast, the threshold current estimator  150  shown in  FIG. 10  estimates the threshold current I th  using the calculated value (U k ) of the drive current I obtained by the drive current calculation section  180 . 
     The light source device  50  shown in  FIG. 10  is further provided with a D/A converter  119  and an A/D converter  149 . The D/A converter  119  executes the D/A (digital to analog) conversion on the signal {circumflex over (X)} k  to output the threshold current command value Dapc 1 . The A/D converter  149  executes the A/D (analog to digital) conversion on the signal L, which is output from the I/V converter  140 , to output the signal Y k . It should be noted that, as described above, since the rate of the temperature response of the semiconductor laser is several tens of microseconds, it is sufficient to set the frequency of the sampling clock for the D/A converter  119 , the A/D converter  149 , and delay devices  281  and  282  which are described more fully below to be about 1 MHz. 
     The threshold current estimator  150  includes five amplifiers  261 - 265 , five computing units  271 - 275 , and two delay devices  281  and  282 . 
     The first delay device  281  delays the signal {circumflex over (X)} k+1  to output the signal {circumflex over (X)} k . The second delay device  282  delays the signal {circumflex over (X)} 0   k+1  to output the signal {circumflex over (X)} 0   k . 
     The first amplifier  261  amplifies the signal U k  β times to output the signal β·U k . The first computing unit  271  subtracts the signal {circumflex over (X)} k  and β·U k  from the signal {circumflex over (X)} 0   k  to output the signal ({circumflex over (X)} 0   k −{circumflex over (X)} k −β·U k ). The second amplifier  262  amplifies the signal ({circumflex over (X)} 0   k −{circumflex over (X)} k −β·U k ) T s /τ obs  times as large to output the signal T s /τ obs ·({circumflex over (X)} 0   k −{circumflex over (X)} k −β·U k ). 
     The third amplifier  263  amplifies the signal (Y k −Ŷ k ) f·T s /τ obs  times to output the signal f·T s /τ obs ·(Y k −Ŷ k ). The second computing unit  272  adds the signal {circumflex over (X)} k  and the signal T s /τ obs ·({circumflex over (X)} 0   k −{circumflex over (X)} k −β·U k ) to each other, and subtracts the signal f·T s /τ obs ·(Y k −Ŷ k ) therefrom. As a result, the second computing unit  272  outputs the signal {circumflex over (X)} k+1  represented by formula (23). 
     The fourth amplifier  264  amplifies the signal (Y k −Ŷ k )f 0 ·T s /τ obs  times to output the signal f 0 ·T s /τ obs ·(Y k −Ŷ k ). The third computing unit  273  subtracts the signal f 0 ·T s /τ obs ·(Y k −Ŷ k ) from the signal {circumflex over (X)} 0   k . As a result, the third computing unit  273  outputs the signal {circumflex over (X)} 0   k+1  represented by formula (23). 
     The fourth computing unit  274  subtracts the signal {circumflex over (X)} k  from the signal U k  to output the signal (U k −{circumflex over (X)} k ). The fifth amplifier  265  amplifies the signal (U k −{circumflex over (X)} k ) M 1  times to output the signal Y k  represented by formula (23). 
     The fifth computing unit  275  subtracts the signal Ŷ k  from the signal Y k  to output the signal (Y k −Ŷ k ). 
     Since the threshold current estimator  150  uses the two state variables X, X 0 , the threshold current estimator  150  is provided with the first delay device  281  for delaying the signal {circumflex over (X)} k+1  at the time point k+1 to obtain the signal {circumflex over (X)} k  at the time point k, and the second delay device  282  for delaying the signal {circumflex over (X)} 0   k+1  at the time point k+1 to obtain the signal {circumflex over (X)} 0   k  at the time point k. The threshold current estimator  150  obtains the signal Ŷ k  using the signals U k  and {circumflex over (X)} k . Further, the threshold current estimator  150  obtains the signal {circumflex over (X)} 0   k+1  provided to the second delay device  282  using the signal (Y k −Ŷ k ) and the signal {circumflex over (X)} 0   k  output from the second delay device  282 . Further, the threshold current estimator  150  obtains the signal {circumflex over (X)} k+1  to be provided to the first delay device  281  using the signal U k , the signal (Y k −Ŷ k ), the signal {circumflex over (X)} k  output from the first delay device  281 , and the signal {circumflex over (X)} 0   k  output from the second delay device  282 . 
     As described above, by using the two state variables X, X 0 , the estimated value {circumflex over (X)} k  of the threshold current can accurately be obtained. 
     The light source device  50  is provided with a comparator  191  and a selector  192  instead of the comparator  171  and the switch  172  ( FIG. 9 ). The comparator  191  compares the signal Ŷ k  with zero. When the signal Ŷ k  is equal to or greater than zero, the comparator  191  makes the selector  192  select the signal (Y k −Ŷ k ). On the other hand, when the signal Ŷ k  is a negative number, the comparator  191  makes the selector  192  select the value of zero. 
     According to the configuration described above, since the feed-back of the signal (Y k −Ŷ k ) to the input of the threshold current estimator  150  is inhibited in the non-emission period similar to the case explained with reference to  FIG. 9 , the threshold current estimator  150  can obtain the estimated value {circumflex over (X)} k  of the threshold current in an open-loop manner. 
     It should be noted that the comparator  191  and the selector  192  in the present embodiment comprise the inhibit section claims recited below. 
     Further, as explained with reference to  FIG. 10 , when the non-emission period is long, the error in the estimated value ({circumflex over (X)} k ) of the threshold current increases gradually. However, when the semiconductor laser  52  starts emitting light again, the threshold current estimator  150  can output the correct estimated value ({circumflex over (X)} k ). It should be noted that a certain recovery time is required before the threshold current estimator  150  outputs the correct estimated value ({circumflex over (X)} k ). Taking the recovery time into consideration, also in the light source device  50  shown in  FIG. 10 , the semiconductor laser  52  is made to emit light preliminarily in the extra period T 0  immediately before the effective period T b  as shown in  FIG. 2 . As described above, by making the semiconductor laser  52  preliminarily emit light immediately before the semiconductor laser  52  starts a significant emission, it becomes possible to correctly obtain the estimated value {circumflex over (x)} of the threshold current immediately after the semiconductor laser  52  starts the significant emission. 
     A-6. DIFFERENTIAL EFFICIENCY ADJUSTMENT SECTION 
       FIG. 11  is a schematic block diagram showing the configuration of the differential efficiency adjustment section  300 . As explained with reference to  FIGS. 5A-5C , the differential efficiency adjustment section  300  sets the grayscale current command value Dapc 2  after adjusting the grayscale current command value Dapc 2 , and in order to execute such an operation, the differential efficiency adjustment section  300  measures a light amount error δ(Y−T), or difference between the target light amount T corresponding to the pixel data D and the actual measured emission amount Y It should be noted that if the number of times of the measurement is few (e.g., only two or three times), there may be errors in the setting value due to measurement error, and therefore, it is preferable to increase the number of times that the measurement is performed in order to successively improve the measurement accuracy. In the present embodiment, a least-square method using a steepest descent method capable of successively and most quickly searching the minimum value of the sum of squares of the light amount errors δ is used. 
     Here, the procedure of setting the pixel data (also referred to as “grayscale values”) D and measuring the actual measured emission amount Y is repeated k times. In this case, it is assumed that the actual measured emission amounts corresponding to the grayscale values {D 1 , D 2 , . . . , D i , . . . , D k } are {Y 1 , Y 2 , . . . , Y i , . . . , Y k }, and the target light amounts corresponding thereto are {T 1 , T 2 , . . . , T i , . . . , T k }, respectively. The evaluation function εk is represented as the sum of squares of the light amount errors as shown in the formula (24) below, and the variable minimizing the evaluation function εk is successively obtained with respect to each value of i. 
     
       
         
           
             
               
                 
                   
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                   ( 
                   24 
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     By obtaining the gradient corresponding to the variation of the variable a, and using the steepest descent method for correcting a in the direction of the gradient, a k  can be represented by the following formula (25). It should be noted that in the formula (25), μ a  is a coefficient. 
     
       
         
           
             
               
                 
                   
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                   ( 
                   25 
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     By assuming that δ i =Y i −T i  is provided in the formula (24), ∂ε k /∂a is represented by the following formula (26). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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                                       i 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ∂ 
                             
                               ∂ 
                               a 
                             
                           
                            
                           
                             { 
                             
                               
                                 ∑ 
                                 
                                   i 
                                   = 
                                   1 
                                 
                                 k 
                               
                                
                               
                                 
                                   ( 
                                   
                                     
                                       a 
                                       * 
                                       
                                         D 
                                         i 
                                       
                                     
                                     + 
                                     b 
                                     - 
                                     
                                       T 
                                       i 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           2 
                           * 
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               k 
                             
                              
                             
                               
                                 ( 
                                 
                                   
                                     a 
                                     * 
                                     
                                       D 
                                       i 
                                     
                                   
                                   + 
                                   b 
                                   - 
                                   
                                     T 
                                     i 
                                   
                                 
                                 ) 
                               
                               * 
                               
                                 D 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           2 
                           * 
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               k 
                             
                              
                             
                               
                                 ( 
                                 
                                   
                                     Y 
                                     i 
                                   
                                   - 
                                   
                                     T 
                                     i 
                                   
                                 
                                 ) 
                               
                               * 
                               
                                 D 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           2 
                           * 
                           
                             
                               ∑ 
                               
                                 i 
                                 = 
                                 1 
                               
                               k 
                             
                              
                             
                               
                                 δ 
                                 i 
                               
                               * 
                               
                                 D 
                                 i 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     Therefore, the following formula (27) is derived from formulas (25) and (26) described above, and by further modifying the formula so as to allow successive calculation, the formulas (28) through (30) described below can be obtained 
     
       
         
           
             
               
                 
                   
                     a 
                     k 
                   
                   = 
                   
                     
                       a 
                       
                         k 
                         - 
                         1 
                       
                     
                     - 
                     
                       
                         μ 
                         a 
                       
                       * 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           k 
                         
                          
                         
                           
                             δ 
                             i 
                           
                           * 
                           
                             D 
                             i 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   
                     δ 
                     k 
                   
                   = 
                   
                     
                       Y 
                       k 
                     
                     - 
                     
                       M 
                       * 
                       
                         D 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
             
               
                 
                   
                     a 
                     k 
                   
                   = 
                   
                     
                       a 
                       
                         k 
                         - 
                         1 
                       
                     
                     - 
                     
                       
                         μ 
                         a 
                       
                       * 
                       S 
                        
                       
                           
                       
                        
                       
                         a 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                      
                     
                         
                     
                      
                     
                       a 
                       k 
                     
                   
                   = 
                   
                     
                       S 
                        
                       
                           
                       
                        
                       
                         a 
                         
                           k 
                           - 
                           1 
                         
                       
                     
                     + 
                     
                       
                         δ 
                         k 
                       
                       * 
                       
                         D 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
           
         
       
     
     Since the variable a is a variable corresponding to the differential efficiency η, it is understood that the differential efficiency η can sufficiently be corrected using the integration value of the products of the light amount error δ k  and the grayscale value D k  as shown in formula (30). 
     Here, the following formula (31) is obtained from the relationship between the drive current I, the threshold current command value Dapc 1 , and the grayscale current command value Dapc 2 , and the relationship between the emission amount L of the semiconductor laser  52 , the drive current I, and the threshold current I th  (see formulas (15) and (16)). 
     
       
         
           
             
               
                 
                   
                     
                       
                         L 
                         = 
                         
                           Y 
                           = 
                             
                            
                           
                             
                               a 
                               * 
                               D 
                             
                             + 
                             b 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           K 
                           * 
                           
                             ( 
                             
                               
                                 
                                   
                                     H 
                                      
                                     
                                         
                                     
                                      
                                     2 
                                   
                                   
                                     H 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
                                 * 
                                 D 
                                  
                                 
                                     
                                 
                                  
                                 apc 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                 * 
                                 D 
                               
                               + 
                               
                                 D 
                                  
                                 
                                     
                                 
                                  
                                 apc 
                                  
                                 
                                     
                                 
                                  
                                 1 
                               
                               - 
                               
                                 
                                   I 
                                   th 
                                 
                                 
                                   H 
                                    
                                   
                                       
                                   
                                    
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
     Note that K is a coefficient. 
     Further, from the definition of Y=a·D+b, the variable a is represented by the following formula (32), and the grayscale current command value Dapc 2  is represented by the formula (33). 
     
       
         
           
             
               
                 
                   a 
                   = 
                   
                     K 
                     * 
                     
                       
                         H 
                          
                         
                             
                         
                          
                         2 
                       
                       
                         H 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     * 
                     D 
                      
                     
                         
                     
                      
                     apc 
                      
                     
                         
                     
                      
                     2 
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
             
               
                 
                   
                     D 
                      
                     
                         
                     
                      
                     apc 
                      
                     
                         
                     
                      
                     2 
                   
                   = 
                   
                     
                       
                         a 
                         · 
                         H 
                       
                        
                       
                           
                       
                        
                       1 
                     
                     
                       
                         K 
                         · 
                         H 
                       
                        
                       
                           
                       
                        
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     By configuring the differential efficiency adjustment section  300  along formulas (28) through (33), the configuration shown in  FIG. 11  may be obtained. The differential efficiency adjustment section  300  is provided with a target generation section  301 , an error calculation section  302 , and a calculation section  310 . It should be noted that the control object  400  is a component (such as the current driver  110 , the semiconductor laser  52 , the light-sensitive element  130 , the I/V converter  140 , or the threshold current estimator  150 ) other than the differential efficiency adjustment section  300  in the light source device  50  shown in  FIG. 10 . In other words, the control object  400  outputs the actual measured emission amount value Y in accordance with the threshold current command value Dapc 1 , the grayscale current command value Dapc 2 , and the grayscale value D. 
     The error calculation section  302  outputs the difference between the target emission amount T(m*D) corresponding to the grayscale value D and supplied from the target generation section  301  and the actual measured emission amount value Y as an output value from the control object  400  to the calculation section  310 . The calculation section  310  is provided with a moment calculation section  303 , a moment integration section  304 , a differential efficiency calculation section  305 , and a grayscale command value calculation section  306 . The moment calculation section  303  multiplies the light amount error δ k  output from the error calculation section  302  by the grayscale value D k (δ k *D k ). The moment integration section  304  integrates the value output by the moment calculation section  303  (as described in formula (30)). The differential efficiency calculation section  305  calculates the variable a using the integration value output by the moment integration section  304  (as described in formula (29)). The grayscale command value calculation section  306  calculates the grayscale current command value Dapc 2  from the variable a (as described in formula (33)), and feeds it back to the control object  400 . 
       FIG. 12A  is a schematic diagram showing a part of the calculation section  310 , where the moment calculation section  303  is omitted. The calculation section  310  shown in  FIG. 12A  can be expressed as the block diagram shown in  FIG. 12B  using first and second delay elements  321  and  323 . It is understood from the diagram that the operation between the input and the output do not vary even if a gain element  320  is moved to form a gain element  324  by integrating the gain elements  320  and  322  as shown in  FIG. 12C . This operation corresponds to modifying of formula (29) described above into the following formula (34), and further replacing of the variable in formula (35) to rewrite it into formula (36). It should be noted that in  FIG. 12C , the first delay element  321  shown in  FIG. 12B  is replaced with the third delay element  325 . 
     
       
         
           
             
               
                 
                   
                     
                       a 
                       k 
                     
                     
                       ( 
                       
                         K 
                         * 
                         H 
                          
                         
                             
                         
                          
                         
                           2 
                           / 
                           H 
                         
                          
                         
                             
                         
                          
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         a 
                         
                           k 
                           - 
                           1 
                         
                       
                       
                         ( 
                         
                           K 
                           * 
                           H 
                            
                           
                               
                           
                            
                           
                             2 
                             / 
                             H 
                           
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                     - 
                     
                       
                         
                           μ 
                           a 
                         
                         
                           ( 
                           
                             K 
                             * 
                             H 
                              
                             
                                 
                             
                              
                             
                               2 
                               / 
                               H 
                             
                              
                             
                                 
                             
                              
                             1 
                           
                           ) 
                         
                       
                       * 
                       S 
                        
                       
                           
                       
                        
                       
                         a 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
             
               
                 
                   
                     A 
                     k 
                   
                   = 
                   
                     
                       a 
                       k 
                     
                     
                       ( 
                       
                         K 
                         * 
                         H 
                          
                         
                             
                         
                          
                         
                           2 
                           / 
                           H 
                         
                          
                         
                             
                         
                          
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
             
               
                 
                   
                     A 
                     k 
                   
                   = 
                   
                     
                       A 
                       
                         k 
                         - 
                         1 
                       
                     
                     - 
                     
                       
                         
                           μ 
                           a 
                         
                         
                           ( 
                           
                             K 
                             * 
                             H 
                              
                             
                                 
                             
                              
                             
                               2 
                               / 
                               H 
                             
                              
                             
                                 
                             
                              
                             1 
                           
                           ) 
                         
                       
                       * 
                       S 
                        
                       
                           
                       
                        
                       
                         a 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     By inserting gain elements into corresponding sections of the circuit shown in  FIG. 12C , and further replacing the second and third delay elements  323  and  325  with first and second flip-flops  327  and  328 , the diagram shown in  FIG. 12D  can be obtained. Here, the gain elements  326   a - 326   d  are used for the gain adjustment in the circuit. If each gain satisfies the following formula (37), the block diagrams shown in  FIGS. 12C and 12D  operate in an equivalent manner. 
     
       
         
           
             
               
                 
                   
                     
                       μ 
                       a 
                     
                     
                       K 
                       · 
                       
                         
                           H 
                            
                           
                               
                           
                            
                           2 
                         
                         
                           H 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   = 
                   
                     
                       1 
                       
                         G 
                          
                         
                             
                         
                          
                         7 
                       
                     
                     · 
                     
                       1 
                       
                         G 
                          
                         
                             
                         
                          
                         1 
                       
                     
                     · 
                     
                       1 
                       
                         G 
                          
                         
                             
                         
                          
                         2 
                       
                     
                     · 
                     
                       1 
                       
                         G 
                          
                         
                             
                         
                          
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
           
         
       
     
     It should be noted that although the output of the flip-flop  327  is a variable obtained by scaling Sa k , and the output of the flip-flop  328  is a variable obtained by scaling a k , they might be referred to collectively as Sa k  in the explanations below in order to avoid complexity. 
     On the premise of the principle of the light amount correction in the present embodiment described above, a detailed configuration of the differential efficiency adjustment section  300  will hereinafter be explained with reference to  FIG. 13 . As shown in  FIG. 13 , the differential efficiency adjustment section  300  is composed of an m-multiplier  331 , a subtracter  332 , a multiplier  333 , a G7-divider  334 , a G3-divider  335 , an adder  336 , a flip-flop  337 , a G2-divider  338 , a subtracter  340 , a flip-flop  341 , and a G1-divider  342 . 
     The m-multiplier  331  outputs the product of grayscale value D i  represented by the grayscale data DR, DG, and DB of the respective colors and the coefficient m, to the subtracter  332  as the target light amount T i (m·D i ). The subtracter  332  outputs the light amount error δ i (=Y i −T i ) obtained by subtracting the target light amount Ti from the light amount measurement value Y i  from the multiplier  333  and the G6-divider  334 . 
     The multiplier  333  outputs the product (hereinafter referred to as a moment MT i ) of the grayscale value D i  and the light amount error δ i  to the G7-divider  334 . The G7-divider  334  outputs the value obtained by dividing the moment MT i  by the coefficient G7 to the G3-divider  335 . The G3-divider  335  outputs the value obtained by dividing the output value (MT i /G7) of the G7-divider  334  by the coefficient G3 to the adder  336 . 
     The adder  336  outputs an additional value obtained by adding the output value (MT i /(G7·G3)) of the G3-divider  335  and the output value of the flip-flop  337  to the D-input terminal of the flip-flop  337 . The flip-flop  337  is a D-type flip-flop, and reflects the input value on the D-input terminal as the output value in sync with a pixel sync clock signal CL. In other words, the adder  336  and the flip-flop  337  form the integration circuit for the moment MT i (δ i ·D i ), and the output value of the flip-flop  337  becomes the integration value of the moment MT i . Hereinafter, the integration value of the moment MT i  is referred to as Sa k . It should be noted that the following is assumed: 
         Sa   k =δ 1   ·D   1 + . . . +δ i   ·D   i + . . . +δ k   ·D   k    
     The G2-divider  338  outputs the value obtained by dividing the integration value Sa k  of the moment MT i  by the coefficient G2 to the subtracter  340 . The subtracter  340  outputs the value obtained by subtracting the output value (Sa k /G2) of the G2-divider  338  from the output value of the flip-flop  341 , to the D-input terminal of the flip-flop  341 . The flip-flop  341  is a D-type flip-flop, and reflects the input value on the D-input terminal as the output value in sync with a pixel sync clock signal CL. In other words, the subtracter  340  and the flip-flop  341  form the correction circuit for calculating the value a k =a k−1 −μ a ·Sa k  represented by formula (29), and the output value of the flip-flop  341  becomes a k . 
     The G1-divider  342  outputs the value obtained by dividing the output value a k  of the flip-flop  341  by the coefficient G1 as the grayscale current command value Dapc 2 . The grayscale current command value Dapc 2  is supplied to the current driver  110  and the threshold current estimator  150 , shown in  FIG. 10 . The threshold current estimator  150  controls the gain M 1  of the fifth amplifier  265  based on the grayscale current command value Dapc 2 . This is because the gain M 1  and the grayscale current command value Dapc 2  have the relationship as described below. 
     Here, it is assumed that the threshold estimation is appropriately executed, meaning that the estimated value {circumflex over (x)} and the threshold current command value Dapc 1  are equal to each other. According to the assumption, the following formula (38) can be obtained from formulas (15) and (16). 
     
       
         
           
             
               
                 
                   
                     M 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     Y 
                     
                       
                         
                           H 
                            
                           
                               
                           
                            
                           2 
                         
                         
                           H 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       * 
                       D 
                        
                       
                           
                       
                        
                       apc 
                        
                       
                           
                       
                        
                       2 
                       * 
                       D 
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
     In other words, it is preferable that the gain M 1  is set having an inversely proportional relationship with the grayscale current command value Dapc 2 . More specifically, it is preferable to set the gain M 1  so as to satisfy the following formula (39) in order to set the emission amount Y to be  510  when the pixel data D takes the maximum value of 255 in the present embodiment. 
     
       
         
           
             
               
                 
                   
                     M 
                      
                     
                         
                     
                      
                     1 
                   
                   = 
                   
                     510 
                     
                       
                         
                           H 
                            
                           
                               
                           
                            
                           2 
                         
                         
                           H 
                            
                           
                               
                           
                            
                           1 
                         
                       
                       * 
                       D 
                        
                       
                           
                       
                        
                       apc 
                        
                       
                           
                       
                        
                       2 
                       * 
                       255 
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
     Incidentally, when the shift in the actual measured emission amount Y with respect to the target light amount T is as shown in  FIG. 14A , there is a possibility that the integration value Sa k  of the products (the moment MT i ) of the light amount error δ i  and the grayscale value D i  approach zero, which substantially stops the adjustment function of the differential efficiency by the differential efficiency adjustment section  300 . In this case, it is preferable to use a difference value (D−D m ) calculated by subtracting an intermediate value D m  in a range from the minimum grayscale value D min  to the maximum grayscale value D max  from the input value D, in obtaining the moment. Thus, it becomes possible to prevent the integration value Sa k  of the moment MT i  from approaching zero. 
     Further, by successively calculating the average value D ave  of the grayscale values, and using a difference value (D−D ave ) calculated by subtracting the average value D ave  from the input value D as a calculation-use grayscale value used in obtaining the moment, it is also possible to prevent the integration value Sa k  of the products (moment values) of the light amount error and the grayscale value from approaching zero, similar to the case described above. In the explanation of this operation using a formula, the integration value of the products of the difference between the grayscale value D k  and the grayscale average value D ave  and the light amount error is calculated using the following formula (40) instead of formula (30). 
         Sa   k   =Sa   k−1 +δ k *( D   k   −D   ave )   (40) 
     In this case, the differential efficiency adjustment section  300  can be configured as shown in  FIG. 15 .  FIG. 15  is substantially the same as  FIG. 13  except that an averaging circuit  350  for successively calculating the average value of the grayscale values D i  and a subtracter  351  for subtracting the output value (the grayscale average value) of the averaging circuit  350  from the grayscale value are disposed on the anterior stage of the multiplier  333 . It should be noted that as the value subtracted from the input value D in obtaining the calculation-use grayscale value, not only the average value of the grayscale value, but also a preset value, for example, a grayscale value of “128” in the case in which the 8-bit grayscale expression is used, may also be used in obtaining the moment. 
     As described above, since the gain M 1  of the fifth multiplier  215  ( FIG. 9 ) is controlled by the grayscale current command value Dapc 2 , the accuracy of the estimation result by the threshold current estimator  150  is improved. As previously described, the threshold current estimator  150  and the differential efficiency adjustment section  300  control the drive current I that is supplied to the semiconductor laser  52  by the current driver  110 . Therefore, as in the case where the real threshold current vary due to the temperature variation, it is possible to make the semiconductor laser  52  accurately emit the light with an intensity which corresponds to the pixel data D. 
     B. MODIFIED EXAMPLES 
     It should be noted that the invention is not limited to the specific examples and the embodiments described above may be modified in various ways without departing from the scope or the spirit of the invention. For example, following modifications may be used in association with the claimed invention. 
     B1. Modified Example 1  
     In the embodiments described above, the differential efficiency adjustment section  300  executes the adjustment of the grayscale current command value Dapc 2 , namely the differential efficiency η, based on the emission amount of the semiconductor laser  52  as actually measured and the pixel data D. It is also possible, however, to arrange that the adjustment of the differential efficiency η using another measurement value. For example, since the differential efficiency η is lowered in accordance with the rise temperature of the semiconductor laser, the control section can also be arranged to execute control so that the current output by the current driver increases in accordance with the temperature of the semiconductor laser. More specifically, it is also possible to arrange that the temperature of the semiconductor laser  52  is measured, and the differential efficiency adjustment section  300  determines the suitable grayscale current command value Dapc 2  corresponding to the measured temperature using a series of predetermined series of values or the like. 
     B2. Modified Example 2  
     Although in the embodiments, the threshold current estimator  150  comprises an observer, it is also possible to arrange that the threshold current estimator  150  estimates the threshold current using other methods. For example, it can be arranged to estimate the threshold current based on the relationship between the actual measured emission amount of the semiconductor laser  52  with respect to the drive current and the differential efficiency calculated by the differential efficiency adjustment section  300 . 
     B3. Modified Example 3  
     In the embodiments described above, for the sake of convenience of explanation, the projector PJ ( FIG. 1 ) is provided with only one light source device  50 . However, the projector may also be provided with, for example, three light source devices for emitting three kinds of colored light beams and a combining optical system for combining the three kinds of colored light beams. Further, the combined light beam may be guided to the polygon mirror  62 . As a result, a color image is displayed on the screen  70 . 
     B4. Modified Example 4  
     In the embodiments described above, the projector PJ is provided with the polygon mirror  62 , and each of the line images included in the image displayed on the screen  70  in one direction. However, an alternate configuration may be used, wherein adjacent line images displayed on the screen  70  are displayed in alternating directions. It should be noted that such a projector is disclosed in, for example, Japanese Patent Publication No. JP-A-2006-227144. Also in this case, it is preferable to provide the extra period in which the preliminary emission of light is executed, immediately before each of the line images is drawn. 
     B5. Modified Example 5  
     Although in the embodiments described above, the light amount correction process is executed during the display operations, there is a possibility that the normal light amount correction may not be achieved if the grayscale value is biased, such as, for example, when an extremely dark image is included in the display. As a counter measure to the case described above, it is possible to arrange that a predetermined grayscale (grayscale data) or a pseudo pixel sync clock signal is generated in the period in which no image display is executed, thereby making the semiconductor laser emit light to execute the light amount correction operation. 
     B6. Modified Example 6  
     When calculating the integration value Sa k  of the moment MT i  in the embodiments described above, since it is preferable to give greater importance to the more recent data (the value of the product of the light amount error and the grayscale value), it is possible to put lower weight on the data further in the past. Specifically, it is sufficient to dispose a weighing constant multiplier in the feed-back path from the output terminal of the flip-flop  337  to the adder  336  shown in  FIG. 13 . The weighing constant is set to be a value smaller than 1 such as ⅞. Thus, the impact of data in the past is sequentially decreased when calculating the integration value Sa k , and therefore, it becomes possible to give weight to the most recent data. Further, although in the embodiments described above, the variable a is successively corrected with the value proportional to the integration value Sa k  of the products (moment values) of the light amount error and the grayscale value, it is also possible to execute a correction of a constant value of the variable a in accordance with the sign of the integration value Sa k . 
     B7. Modified Example 7  
     Although in the embodiments described above, the light source device according to the invention is applied to the so-called raster scan type projector, the light source device may also be used in a projector provided with a light modulation device such as a liquid crystal panel or DMD (Digital Micromirror Device, a trademark of Texas Instruments). In this case, it is sufficient to provide a constant value as the signal D, for example. 
     Further, although in the embodiments descried above, the invention is applied to the projection type image display device, the invention can also be applied to a direct view type image display device. 
     B8. Modified Example 8  
     Although in the embodiments described above, the light source device  50  is applied to the projector PJ, the light source devices can also be applied to other optical devices such as processing equipment instead of the projector PJ. 
     B9. Modified Example 9  
     Although the light source device  50  is provided with the semiconductor laser in the embodiments described above, it is also possible to provide the light source device with another solid-state light source (semiconductor light emitting element) such as a light emitting diode (LED) instead of the semiconductor laser. 
     B10. Modified Example 10  
     In the embodiments described above, it is possible to replace a part of the configuration realized by hardware with software, or to replace a part of the configuration realized by software with hardware.