Exhibit 3.1

RESTATED

CERTIFICATE OF INCORPORATION

OF

BRUKER CORPORATION

FIRST:    The name of this corporation shall be: Bruker Corporation.

SECOND:    Its registered office in the State of Delaware is to be located at 251 Little Falls Drive, Wilmington, County of New Castle, 19808, and its registered agent at such address is: CORPORATION SERVICE COMPANY.

THIRD:    The purpose or purposes of the corporation shall be:

To carry on any and all business and to engage in any lawful act or activity for which corporations may be organized under the General Corporation Law of Delaware.

FOURTH:    The total number of shares of stock which the Corporation shall have authority to issue is 265,000,000 shares, which shares shall be divided into two classes consisting of: (i) 260,000,000 shares of Common Stock (with $.01 par value per share) (“Common Stock”) and (ii) 5,000,000 shares of Preferred Stock (with $.01 par value per share) (“Blank Check Preferred Stock”).

The designations and the powers, preferences and rights, and the qualifications, limitations or restrictions of the Common Stock and the Blank Check Preferred Stock shall be as follows:

A.  COMMON STOCK

1.    Voting Rights.    Except as otherwise required by law or this Restated Certificate of Incorporation (this “Certificate of Incorporation”), each holder of Common Stock shall have one vote in respect of each share of Common Stock held by him of record on the books of the Corporation for the election of directors and on all matters submitted to a vote of stockholders of the Corporation.

2.    Dividends.    The holders of shares of Common Stock shall be entitled to receive, when and if declared by the Board of Directors, out of the assets of the Corporation which are by law available therefor, dividends payable either in cash, in property or in shares of capital stock, subject, however, to the limitations contained in Part B below.

3.    Dissolution, Liquidation or Winding Up.    After distribution in full of the preferential amount, if any, to be distributed to the holders of series of the Blank Check Preferred Stock (in accordance with the relative preferences among such series) in the event of involuntary liquidation, distribution, dissolution or winding-up, of the Corporation, the holders of the

Common Stock shall be entitled to receive all of the remaining assets of the Corporation, tangible and intangible, or whatever kind available for distribution to stockholders, ratably in proportion to the number of shares of Common Stock held by them respectively.

B.   BLANK CHECK PREFERRED STOCK

1.    Issuance.    Shares of Blank Check Preferred Stock may be issued from time to time in one or more series as designated by the Board of Directors, each of said series to be distinctly designated. Shares of Blank Check Preferred Stock may be issued when deemed by the Board of Directors to be necessary to protect the Corporation from an actual, threatened or potential hostile or undesired takeover or takeover attempt. All shares of any one series of the Blank Check Preferred Stock shall be alike in every particular, except that there may be different dates from which dividends, if any, thereon shall be cumulative, if made cumulative. The voting powers, if any, and the designations, relative preferences, participating, optional or other special rights or privileges of each such series, and the qualifications, limitations or restrictions thereof, if any, may differ from those of any and all other series at any time outstanding.

2.    Authority of the Board of Directors.    The Board of Directors is authorized, subject to limitations prescribed by law and the provisions of this Article FOURTH, to provide for the issuance of the shares of the Blank Check Preferred Stock in series, and by filing a certificate pursuant to the applicable law of the State of Delaware, to establish from time to time the number of shares to be included in each such series, and to fix in the resolution or resolutions providing for the issue of such stock adopted by the Board of Directors of the Corporation the voting powers, if any, and the designations, relative preferences, participating, optional or other special rights or privileges, and the qualifications, limitations or restrictions of such series, including, but without limiting the generality of the foregoing, the following:

(a)    The distinctive designation of, and the number of shares of the Blank Check Preferred Stock which shall constitute such series. The designation of a series of preferred stock need not include the words “preferred” or “preference” and may be designated “special” or other distinctive term. Unless otherwise provided in the resolution issuing such series, the number of shares of any series of the Blank Check Preferred Stock may be increased or decreased (but not below the number of shares thereof then outstanding) by the Board of Directors in the manner prescribed by law;

(b)    The rate and times at which, and the terms and conditions upon which, dividends, if any, on the Blank Check Preferred Stock of such series shall be paid, the extent of the preference or relation, if any, of such dividends to the dividends payable on any other class or classes, or series of the same or other classes of stock and whether such dividends shall be cumulative or non-cumulative and, if cumulative, the date from which such dividends shall be cumulative;

(c)    Whether the series shall be convertible into, or exchangeable for, at the option of the holders of the Blank Check Preferred Stock of such series or the Corporation or upon the happening of a specified event, shares of any other class

or classes or any other series of the same or any other class or classes of stock of the Corporation, and the terms and conditions of such conversion or exchange, including provisions for the adjustment of any such conversion rate in such events as the Board of Directors shall determine;

(d)    Whether or not the Blank Check Preferred Stock of such series shall be subject to redemption at the option of the Corporation or the holders of such series or upon the happening of a specified event, and the redemption price or prices and the time or times at which, and the terms and conditions upon which, the Blank Check Preferred Stock of such series may be redeemed;

(e)    The rights, if any, of the holders of the Blank Check Preferred Stock of such series upon the voluntary or involuntary liquidation, merger, consolidation, distribution or sale of assets, dissolution or winding-up, of the Corporation;

(f)    The terms of the sinking fund or redemption or purchase account, if any, to be provided for the Blank Check Preferred Stock of such series; and

(g)    Subject to subparagraph 5 of Paragraph C hereof, whether such series of the Blank Check Preferred Stock shall have full, limited or no voting powers including, without limiting the generality of the foregoing, whether such series shall have the right, voting as a series by itself or together with other series of the Blank Check Preferred Stock or all series of the Blank Check Preferred Stock as a class, to elect one or more directors of the Corporation if there shall have been a default in the payment of dividends on any one or more series of the Blank Check Preferred Stock or under such other circumstances and on such conditions as the Board of Directors may determine.

C.   OTHER PROVISIONS.

1.    No holder of any of the shares of any class or series of stock or of options, warrants or other rights to purchase shares of any class or series of stock or of other securities of the Corporation shall have any preemptive right to purchase or subscribe for any unissued stock of any class or series or any additional shares of any class or series to be issued by reason of any increase of the authorized capital stock of the Corporation of any class or series, or bonds, certificates of indebtedness, debentures or other securities convertible into or exchangeable for stock of the Corporation of any class or series, or carrying any right to purchase stock of any class or series, but any such unissued stock, additional authorized issue of shares of any class or series of stock or securities convertible into or exchangeable for stock, or carrying any right to purchase stock, may be issued and disposed of pursuant to resolution of the Board of Directors to such persons, firms, corporations or associations (including such holders or others) and upon such terms as may be deemed advisable by the Board of Directors in the exercise of its sole discretion.

2.    The relative powers, preferences and rights of each series of the Blank Check Preferred Stock in relation to the powers, preferences and rights of each other series of the Blank Check

Preferred Stock shall, in each case, be as fixed from time to time by the Board of Directors in the resolution or resolutions adopted pursuant to authority granted in Paragraph B hereof. The consent, by class or series vote or otherwise, of the holders of such of the series of the Blank Check Preferred Stock as are from time to time outstanding shall not be required for the issuance by the Board of Directors of any other series of the Blank Check Preferred Stock whether or not the powers, preferences and rights of such other series shall be fixed by the Board of Directors as senior to, or on a parity with, the powers, preferences and rights of such outstanding series, or any of them; provided, however, that the Board of Directors may provide in the resolution or resolutions as to any series of the Blank Check Preferred Stock adopted pursuant to Paragraph B hereof, the conditions, if any, under which the consent of the holders of a majority (or such greater proportion as shall be fixed therein) of the outstanding shares of such series shall be required for the issuance of any or all other series of the Blank Check Preferred Stock.

3.    Subject to the provisions of subparagraph 2 of this Paragraph C, shares of any series of the Blank Check Preferred Stock may be issued from time to time as the Board of Directors of the Corporation shall determine and on such terms and for such consideration as shall be fixed by the Board of Directors.

4.    Shares of authorized Common Stock may be issued from time to time as the Board of Directors of the Corporation shall determine and on such terms and for such consideration as shall be fixed by the Board of Directors.

5.    The number of authorized shares of Common Stock and of the Blank Check Preferred Stock, without a class or series vote, may be increased or decreased from time to time (but not below the number of shares thereof then outstanding) by the affirmative vote of the holders of a majority of the stock of the Corporation entitled to vote thereon.

FIFTH:    The number of Directors shall be fixed from time to time exclusively by the Board of Directors pursuant to a resolution adopted by the Board of Directors. The Directors of the Corporation shall be divided into three classes: Class I, Class II and Class III. Each class shall consist, as nearly as may be possible, of one-third of the whole number of the Board of Directors. If the Board of Directors is not evenly divisible by three, the Board of Directors shall determine the number of Directors to be elected to each class. The initial members of Class I shall hold office for a term to expire at the Annual Meeting of the Stockholders to be held in 2001; the initial members of Class II shall hold office for a term to expire at the Annual Meeting of the Stockholders to be held in 2002, the initial members of Class III shall hold office for a term to expire at the Annual Meeting of the Stockholders to be held in 2003, and in the case of each class, until their respective successors are duly elected and qualified. At each annual election held commencing with the annual election in 2001, the Directors elected to succeed those whose terms expire shall be identified as being of the same class as the Directors they succeed and shall be elected to hold office for a term to expire at the third Annual Meeting of the Stockholders after their election, and until their respective successors are duly elected and qualified. If the number of Directors changes, any increase or decrease in Directors shall be apportioned among the classes so as to maintain all classes as equal in number as possible, and any additional Director elected to any class shall hold office for a term which shall coincide with the terms of the other Directors in such class and until his successor is duly elected and qualified.

SIXTH:     In furtherance and not in limitation of the powers conferred by the laws of the State of Delaware:

A.        The Board of Directors of the corporation is expressly authorized to adopt, amend, or repeal the by-laws of the Corporation.

B.         Elections of Directors need not be by written ballot unless the by-laws of the corporation shall so provide.

C.         The books of the Corporation may be kept at such place within or without the State of Delaware as the by-laws of the Corporation may provide or as may be designated from time to time by the Board of Directors of the Corporation.

SEVENTH:    Whenever a compromise or arrangement is proposed between this corporation and its creditors or any class of them and/or between this corporation and its stockholders or any class of them, any court of equitable jurisdiction within the State of Delaware may, on the application in a summary way of this corporation or of any creditor or stockholder thereof or on the application of any receiver or receivers appointed for this corporation under the provisions of section 291 of Title 8 of the Delaware Code or on the application of trustees in dissolution or of any receiver or receivers appointed for this corporation under the provisions of section 279 of Title 8 of the Delaware Code, order a meeting of the creditors or class of creditors, and/or of the stockholders or class of stockholders of this corporation, as the case may be, to be summoned in such manner as the said court directs. If a majority in number representing three-fourths in value of the creditors or class of creditors, and/or of the stockholders or class of stockholders of this corporation, as the case may be, agree to any compromise or arrangement and to any reorganization of this corporation as a consequence of such compromise or arrangement, the said compromise or arrangement and the said reorganization shall, if sanctioned by the court to which the said application has been made, be binding on all the creditors or class of creditors, and/or on all the stockholders or class of stockholders, of this corporation, as the case may be, and also on this corporation.

EIGHTH:    The Corporation hereby elects in this Certificate of Incorporation not to be governed by Section 203 of the General Corporation Law of Delaware.

NINTH:    Except as stated in Article Tenth of this Certificate of Incorporation, the corporation reserves the right to amend or repeal any provision contained in this certificate of incorporation, in the manner now or hereafter prescribed by statute, and all rights conferred upon a stockholder herein are granted subject to this reservation.

TENTH:    No director shall be personally liable to the corporation or its stockholders for monetary damages for breach of fiduciary duty as a director notwithstanding any provision of law imposing such liability; provided, however, that, to the extent required by applicable law, this provision shall not eliminate the liability of a director (i) for any breach of the director’s duty of loyalty to the corporation or its stockholders, (ii) for acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law, (iii) under Section 174 of the General Corporation Law of Delaware, or (iv) for any transaction from which the director derived an improper personal benefit. No amendment to or repeal of this provision shall apply to

or have any effect on the liability or alleged liability of any director for or with respect to any acts or omissions of such director occurring prior to such amendment or repeal.

ELEVENTH:    The Corporation is to have perpetual existence.